AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the center of the circle is :

In Fig. 10.3, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to:

If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is:

In Fig.10.4, if ABC = 20 �, then AOC is equal to:

In Fig.10.5, if AOB is a diameter of the circle and AC = BC, then CAB is equal to:

In Fig. 10.6, if OAB = 40 �, then ACB is equal to:

In Fig. 10.7, if DAB = 60 �, ABD = 50 �, then ACB is equal to:

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ADC = 140 �, then BAC is equal to:

In Fig. 10.8, BC is a diameter of the circle and BAO = 60 �. Then ADC is equal to:

In Fig. 10.9, AOB = 90 � and ABC = 30 �, then CAO is equal to:

Two chords AB and CD of a circle are each at distances 4 cm from the center. Then AB = CD.

Two chords AB and AC of a circle with center O are on the opposite sides of OA. Then OAB = OAC.

Two congruent circles with centers O and O’ intersect at two points A and B. Then AOB = AO’B.

Through three collinear points a circle can be drawn.

A circle of radius 3 cm can be drawn through two points A, B such that AB = 6 cm.

If AOB is a diameter of a circle and C is a point on the circle, then AC^{2} + BC^{2} = AB^{2}

ABCD is a cyclic quadrilateral such that A = 90°, B = 70°, C = 95° and D = 105°.

If A, B, C, D are four points such that BAC = 30° and BDC = 60°, then D is the center of the circle through A, B and C.

If A, B, C and D are four points such that BAC = 45° and BDC = 45°, then A, B, C, D are con cyclic.

In Fig. 10.10, if AOB is a diameter and ADC = 120°, then CAB = 30°

If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.

If the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA ≅ Arc PYB.

A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are concurrent.

AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC passes through the center of the circle.

If a line segment joining mid-points of two chords of a circle passes through the center of the circle, prove that the two chords are parallel.

ABCD is such a quadrilateral that A is the center of the circle passing through B, C and D. Prove that ∠CBD + ∠CDB = ∠BAD.

O is the circumcenter of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.

On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that ∠BAC = ∠BDC.

Two chords AB and AC of a circle subtends angles equal to 90° and 150°, respectively at the center. Find ∠BAC, if AB and AC lie on the opposite sides of the center.

If BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC, prove that the points B, C, M and N are con cyclic.

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral so formed is cyclic.

If a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are also equal.

The circumcenter of the triangle ABC is O. Prove that ∠OBC + ∠BAC = 90°.

A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in major segment.

In Fig.10.13, ∠ADC = 130° and chord BC = chord BE. Find ∠CBE.

In Fig.10.14, ∠ACB = 40°. Find ∠OAB.

A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and ∠ADC = 130°. Find ∠BAC.

Two circles with centers O and O’ intersect at two points A and B. A line PQ is drawn parallel to OO’ through A(or B) intersecting the circles at P and Q. Prove that PQ = 2 OO’.

In Fig.10.15, AOB is a diameter of the circle and C, D, E are any three points on the semi-circle. Find the value of ∠ACD + ∠BED.

In Fig. 10.16, ∠OAB = 30° and ∠OCB = 57°. Find ∠BOC and ∠AOC.