Question

In the picture, a circle is drawn with a line as diameter and a smaller circle with half the line as diameter. Prove that any chord of the larger circle through the point where the circles meet is bisected by the small circle.

Answer 1

∠ADO = ∠APB = 90° 

(angle subtended by diameter is always 90°)

⇒ OD\\PB

AO = OB (Radius of bigger circle)

(If in a triangle, the line drawn from midpoint of one side, is parallel to another side, then the line will bisect the third side) 

Therefore AD = DP 

(AB’s midpoint is ‘O’ and OD\\PB)