A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the center of the circle.

Find the length of a chord which is at a distance of 3 cm from the center of a circle of radius 5 cm.

A chord of a length 30 cm is drawn at a distance of 8 cm from the center of a circle. Find out the radius of the circle.

In a circle of radius 5 cm, and are two parallel chords of lengths 8 cm and 6 cm respectively. calculate the distance between the chords if they are

(i) on the same side of the center

(ii) on the opposite sides of the center.

Two parallel chords of lengths 30 cm and 16cm are drawn on the opposite sides of the center of a circle of radius 17 cm. Find the distance between the chords.

In the given figure, the diameter of a circle with center is perpendicular to chord If and calculate the radius of the circle.

In the given figure, a circle with center is given in which a diameter bisects the chord at a point such that and Find the radius of the circle.

In the adjoining figure, is perpendicular to the chord of a circle with center If is a diameter, show that and

In the given figure, is the center of a circle in which chords and intersect at such that bisects Prove that

Prove that the diameter of a circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it.

Prove that two different circles cannot intersect each other at more than two points.

Two circles of radii 10 cm and 8 cm intersect each other, and the length of the common chord is 12 cm. Find the distance between their centers.

Two equal circles intersect in and A straight line through meets the circles in and Prove that

If a diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.

In the adjoining figure, two circles with centers at and and of radii 5 cm and 3 cm touch each other internally. If the perpendicular bisector of meets the bigger circle in and find the length of

In the given figure, is a chord of a circle with center and is produced to such that Also, is joined and produced to meet the circle in If and prove that

In the adjoining figure, is the center of a circle. If and are chords of the circle such that and prove that

In the adjoining figure, is a diameter of a circle with center If and are two chord such that prove that

An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.

In the adjoining figure, and are two equal chords of a circle with center Show that lies on the bisector of

In the adjoining figure, is a square. A circle drawn with center cuts the suare in and Prove that

(i) In Figure (1), is the center of the circle. If and find (ii) In figure (2), and are three points on the circle with center such that and Find

In the given figure, is the center of the circle and

Calculate the values of (i) (ii)

In the given figure, is the center of the circle. If and find the value of

In the given figure, is the center of the circle. If and find

In the given figure, is the center of the circle. If find

In the given figure, and calculate

(i) (ii) (iii)

In the adjoining figure, is a chord parallel to diameter of the circle with center If calculate

In the adjoining figure, is the center of a circle. Chord is parallel to diameter If calculate

In the given figure, and are straight lines through the center of a circle. If and find (i) (ii)

In the adjoining figure, is the center of a circle, and find

In the adjoining figure, chords and of a circle with center intersect at right angles at If calculate

In the given figure, is the center of a circle in whichand Find (i) (ii)

In the given figure, Show that is equal to the radius of the circumcircle of whose center is O.

In the given figure, is a diameter of a circle with center If and find and

In the given figure, is a cyclic quadrilateral whose diagonals intersect at such that and Find (i) (ii)

In the given figure, is a diameter and is a cyclic quadrilateral. If find

In the given figure, is a cyclic quadrilateral in which

If find

(i) (ii) (iii)

In the given figure, is the center of the circle and arc subtends an angle of 130° at the center. If is extended to find

In the given figure, is a cyclic quadrilateral in which is drawn parallel to and is produced. If and find

In the given figure, and find

In the given figure, is the center of the given circle and measure of arc is 100°. Determine and

In the given figure, is equilateral. Find (i) (ii)

In the adjoining figure, is a cyclic quadrilateral in which and Find

In the given figure, is the center of a circle and Find the values of and

In the given figure, is the center of a circle and Find the values of and

In the given figure, sides and of cyclic quadrilateral are produced to and respectively.

If and find the value of

In the given figure, is a diameter of a circle with center and

If calculate

(i) (ii)

(iii) (iv)

Also, show that is an equilateral triangle.

Two chords and of a circle intersect each other at outside the circle. If and find

In the given figure, is the center of a circle. If and calculate

(i) (ii)

In the given figure, is a cyclic quadrilateral whose sides and are produced to meet in

Prove that

In the given figure, is an isosceles triangle in which and a circle passing through and intersects and at and respectively.

Prove that

is an isosceles triangle in which If and are midpoints of and respectively, prove that the points are concyclic.

Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.

Prove that the circles described with the four sides of a rhombus, as diameters, pass through the point of intersection of its diagonals.

is a rectangle. Prove that the center of the circle through is the point of intersection of its diagonals.

Give a geometrical construction for finding the fourth point lying on a circle passing through three given points, without finding the center of the circle. Justify the construction.

In a cyclic quadrilateral if show that the smaller of the two is 60°.

In the given figure, is a quadrilateral in which and Show that the points lie on a circle.

In the given figure, and

Find the values of and

The diagonals of a cyclic quadrilateral are at right angles. Prove that the perpendicular from the point of their intersection on any side when produced backwards, bisects the opposite side.

In the given figure, chords and of a circle are produced to meet at Prove that and are similar.

In the given figure, and are two parallel chords of a circle. If and are straight lines, intersecting at prove that is isosceles.

In the given figure, is a diameter of a circle with center If and are straight lines, meeting at such that and find

(i) (ii) (iii)

The radius of a circle is 13 cm and the length of one of its chords is 10 cm. The distance of the chord from the centre is

A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of the chord is

In the given figure, BOC is a diameter of a circle and AB = AC. Then, ∠ABC = ?

In the given figure, O is the centre of a circle and ∠ACB = 30°. Then, ∠AOB = ?

In the given figure, O is a centre of a circle. If ∠OAB = 40° and C is a point on the circle, then ∠ACB = ?

In the given figure, AOB is a diameter of a circle with centre O such that AB = 34 cm and CD is a chord of length 30 cm. Then, the distance of CD from AB is

AB and CD are two equal chords of a circle with centre O such that ∠AOB = 80°, then ∠COD = ?

In the given figure, CD is the diameter of a circle with centre O and CD is perpendicular to chord AB. If AB = 12 cm and CE = 3 cm, then radius of the circle is

In the given figure, O is the centre of a circle and diameter AB bisects the chord CD at a point such that CE = ED = 8cm and EB = 4 cm. The radius of the circle is

In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB || CD. If AB = 10 cm, then CD = ?

In the given figure, AB is a chord of a circle with centre O and AB is produced to C such that BC = OB. Also, CO is joined and produced to meet the circle in D. If ∠AOC = 25° ∠ACD = 25°, then ∠AOD = ?

In the given figure, AB is a chord of a circle with centre O and BOC is a diameter. If OD ⊥ AB such that OD = 6cm then AC = ?

An equilateral triangle of side 9 cm is inscribed in a circle. The radius of the circle is

The angle in a semicircle measures

Angles in the same segment of a circle area are

In the given figure, ΔABC and ΔDBC are inscribed in a circle such that ∠BAC = 60° and ∠DBC = 50°. Then, ∠BCD = ?

In the given figure, BOC is a diameter of a circle with centre O. If ∠BCA = 30°, then ∠CDA = ?

In the given figure, O is the centre of a circle. If ∠OAC = 50°, then ∠ODB = ?

In the given figure, O is the centre of a circle in which ∠OBA = 20° and ∠OCA = 30°. Then, ∠BOC = ?

In the given figure, O is the centre of a circle. If ∠AOB = 100° and ∠AOC = 90°, then ∠BAC = ?

In the given figure, O is the centre of a circle. Then, ∠OAB = ?

In the given figure, O is the centre of a circle and ∠AOC = 120°. Then, ∠BDC = ?

In the given figure, O is the centre of a circle and ∠OAB = 50°. Then, ∠CDA = ?

In the give figure, and are two intersecting chords of a circle. If ∠CAB = 40° and ∠BCD = 80°, then ∠CBD = ?

In the given figure, O is the centre of a circle and chords AC and BD intersect at E. If ∠AEB = 110° and ∠CBE = 30° then ∠ADB = ?

In the given figure, O is the centre of a circle in which ∠OAB = 20° and ∠OCB = 50°. Then, ∠AOC = ?

In the given figure, AOB is a diameter and ABCD is a cyclic quadrilateral. If ∠ADC = 120°, then ∠BAC = ?

In the given figure, ABCD is a cyclic quadrilateral in which AB || DC and ∠BAD = 100°. Then ∠ABC = ?

In the given figure, O is the centre of a circle and ∠AOC = 130°. Then, ∠ABC = ?

In the given figure, AOB is a diameter of a circle and CD || AB. If ∠BAD = 30°, then ∠CAD = ?

In the given figure, O is the centre of a circle in which ∠AOC = 100°. Side AB of quad. OABC has been produced to D. Then, ∠CBD = ?

In the given figure, O is the centre of a circle and ∠ = 50°. Then, ∠BOD = ?

In the given figure, ABCD is a cyclic quadrilateral in which BC = CD and ∠CBD = 35°. Then, ∠BAD = ?

In the given figure, equilateral ΔABC is inscribed in a circle and ABDC is a quadrilateral, as shown. Then, ∠BDC = ?

In the given figure, sides AB and AD of quad. ABCD are produced to E and F respectively. If ∠CBE = 100°, then ∠CDF = ?

In the given figure, O is the centre of a circle and ∠AOB = 140°. Then, ∠ACB = ?

In the given figure, O is the centre of a circle and ∠AOB = 130°. Then, ∠ACB = ?

In the given figure, ABCD and ABEF are two cyclic quadrilaterals. If ∠BCD = 110°, then ∠BEF = ?

In the given figure, ABCD is a cyclic quadrilateral in which DC is produced to E and CF is drawn parallel to AB such that ∠ADC = 90° and ∠ECF = 20°. Then, ∠BAD = ?

Two chords AB and CD of a circle intersect each other at a point E outside the circle. If AB = 11 cm, BE = 3 cm and DE = 3.5 cm, then CD = ?

In the given figure, A and B are the centers of two circles having radii 5 cm and 3 cm respectively and intersecting at points P and Q respectively. If AB = 4 cm, then the length of common chord PQ is

In the given figure, ∠AOB = 90° and ∠ABC = 30°. Then, ∠CAO = ?

Three statements are given below:

I. If a diameter of a circle bisects each of the two chords of a circle, then the chords are parallel.

II. Two circles of radii 10 cm and 17 cm intersect each other and the length of the common chord is 16 cm. Then, the distance between their centres is 23 cm.

III. ∠ is the line intersecting two concentric circles with centre O at points A, B, C and D as shown. Then, AC = DB.

Which is true?

Two statements I and II are given and a question is given. The correct answer is

Is ABCD a cyclic quadrilateral?

I. Points A, B, C and D lie on a circle.

II. ∠B + ∠D = 180°.

Two statements I and II are given and a question is given. The correct answer is

Is ΔABC right – angled at B?

I. ABCD is a cyclic quadrilateral.

II. ∠D = 90°.

The question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer:

The question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer:

The question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer:

The question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer:

The question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer:

The question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer:

Write T for true and F for false

(i) The degree measures of a semicircle is 180^o.

(ii) The perimeter of a circle is called its circumference.

(iii) A circle divides the plane into three parts.

(iv) Let O be the centre of a circle with radius r. Then a point P such that OP < r is called an interior point of the circle.

(v) A circle can have only a finite number of equal chords.

Match the following columns:

The correct answer is:

(a) – ……, (b) – ………,

(c) – …….., (d) – ………,

Fill in the blanks

(i) Two circles having the same centre and different radii are called ________ circles.

(ii) Diameter is the _________ chord of a circle.

(iii) A continuous piece of a circle is called the ________ of the circle.

(iv) An arc of a circle is called a __________ if the ends of the arc are the ends of a diameter.

(v) A segment of a circle is the region between an arc and a ________ of the circle.

(vi) A line segment joining the centre to any point on the circle is called its ________.

In the given figure, ∠ECB = 40° and ∠CEB = 105°. Then, ∠EAD = ?

In the given figure, O is the centre of a circle, ∠AOB = 90° and ∠ABC = 30°. Then, ∠CAO = ?

In the given figure, O is the centre of a circle. If ∠OAB = 40°, then ∠ACB = ?

In the given figure, ∠DAB = 60° and ∠ABD = 50°, then ∠ACB = ?

In the given figure, O is the centre of a circle, BC is a diameter and ∠BAO = 60°. Then, ∠ADC = ?

Find the length of a chord which is at a distance of 9 cm from the centre of a circle of radius 15 cm.

Prove that equal chords of a circle are equidistant from the centre.

Prove that an angle in a semicircle is a right angle.

Prove that a diameter is the largest chord in a circle.

A circle with centre O is given in which ∠OBA = 30° and ∠OCA = 40°. Find ∠BOC.

In the given figure, AOC is a diameter of a circle with centre O and arc arc BYC. Find ∠BOC.

In the given figure, O is the centre of a circle and ∠ABC = 45°. Prove that OA ⊥ OC.

In the given figure, O is the centre of a circle, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.

In the given figure, O is the centre of a circle, ∠ACB = 40°. Find ∠OAB.

In the given figure, O is the centre of a circle, ∠OAB = 30° and ∠OCB = 55°. Find ∠BOC and ∠AOC.

In the given figure, O is the centre of the circle, BD = OD and CD ⊥ AB. Find ∠CAB.

In the given figure, ABCD is a cyclic quadrilateral. A circle passing through A and B meets AD and BC in the points E and F respectively. Prove that EF || DC.

In the given figure, AOB is a diameter of the circle and C, D, E are any three points on the semicircle. Find the value of ∠ACD + ∠BED.

In the given figure, O is the centre of a circle and ∠BCO = 30°. Find x and y.

PQ and RQ are the chords of a circle equidistant from the centre. Prove that the diameter passing through Q bisects ∠PQR and ∠PSR.

Prove that there is one and only one circle passing through three non – collinear points.

In the give figure, OPQR is a square. A circle drawn with centre O cuts the square in x and y. Prove that QX = XY.

In the given figure, AB and AC we two equal chords of a circle with centre O. Show that O lies on the bisectors of ∠BAC.