Question

A smaller circle touches internally to a larger circle at A and passes
through the centre of the larger circle. O is the centre of the larger circle
and BA, OA are the diameters of the larger and smaller circles
respectively. Chord AC intersects the smaller circle at a point D. If AC = 12
cm, then AD is:
B
C​

Answer 1

Given : A smaller circle touches internally to a larger circle at A and

passes through the center of the larger circle.

O is the center of the larger circle and BA, OA are of the diameters of the larger and smaller circles respectively.

Chord AC intersects the smaller circle at a point D.  AC = 12 cm,  

To Find : length of  AD  

Solution:

Compare ΔAOD and ΔABC

∠A = ∠A  common

∠ADO = ∠ACB  = 90°    as   OA  and AB are Diameter

=> ΔAOD ~ ΔABC

=> AO/AB  = AD/AC

AO/AB = 1/2  

=> 1/2  = AD/12

=> AD = 6 cm

AD is  6 cm

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