Question

Circles with centres P and Q intersect at points A and B as shown in the figure. CBD is a line segment and EBM is tangent to the circle, with centre Q, at point B. If the circle are congruent; show that CE = BD.

Answer 1

Join AB and AD

EBM is a tangent and BD is a chord.

∠DBM = ∠BAD  ...(Angles in alternate segments)

But, ∠DBM = ∠CBE  ...(Vertically opposite angles)

∴ ∠BAD = ∠CBE

Since in the same circle or congruent circles, if angles are equal, then chords opposite to them are also equal.

Therefore, CE = BD