Question

15. 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; show that : CE = BD.​

Answer 1

Step-by-step explanation:

To solve this we need to draw construct a diagram for it.

Check the attached file for the diagram....

Construction :_

Joining AD and AB

After the construction see that ABD and BEM becomes two triangles..

∠DBM=∠BAD  (Angles in alternate segments are always equal)

∠DBM=∠CBE  (Vertically Opposite Angles)

∴ ∠CBE = ∠BAD

In any congruent circle if any angle is equal then the chord opposite to it also becomes equal.

Here, ∠CBE = ∠BAD

So, chords opposite to the angles are CE and BD respectively..

∴ CE = BD

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