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 circles are congruent; Then, CE = ________

• A. BD
• B. 3BD
• C. 7BD
• D. 2BD

Answer 1

The correct option is A

BD

Given Two circles with centres P and Q intersect each other at A and B. CBD is a line segment and EBM is tangent to the circle with centre Q, at B. Radii of the circles are equal.

Construction - Join AB and AD

Proof - EBM is the tangent and BD is the chord

$\therefore \angle DBM=\angle BAD$ (Angles in alt. segment)

But $\angle DBM=\angle CBE$

(Vertically opposite angles)

$\therefore \angle BAD=\angle CBE$

$\because$ In the same circle congruent circles, if angles are equal, then chords opposite to them are also equal.

$\therefore CE=BD$