Question

In the adjoining figure, circles with centres C and D touch internally at point E. D lies on the inner circle. Chord EB of the outer circle intersects inner circle at point A. Prove that, seg EA ≅ seg AB.

Answer 1

Given: Circles with centres C and D touch each other internally. 

To prove: seg EA ≅ seg AB 

Construction: Join seg ED and seg DA. 

Proof: 

E – C – D [Theorem of touching circles] 

seg ED is the diameter of smaller circle. 

∴∠EAD = 90° [Angle inscribed in a semicircle]

∴ seg AD ⊥ chord EB 

∴ seg EA ≅ seg AB [Perpendicular drawn from the centre of the circle to the chord bisects the chord]