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?


Here, Clearly I and III are correct.


Let us check for II statement



Construction: Let B and C be the centers of two circles having radii 10cm and 17 cm respectively and let AD be the common chord cutting BC at E.


Here,


AE = ED = 8cm


Now, in ΔABE


BE2 = AB2 – AE2


BE2 = (10)2 – (8)2


BE2 = 100– 64 = 36


BE = 6cm


Now, in ΔAEC


EC2 = AC2 – AE2


EC2 = (17)2 – (8)2


EC2 = 289– 64 = 225


EC = 25cm


Here,


BC = BE + EC = 6 + 15 = 21cm


But, it is given BC = 23cm


∴ Statement II is false

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