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.

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Solution

we have the following diagram

After joining AB and AD , we get the △ABD
EBM is a tangent and BD is a chord.
$∠ D B M = ∠ B A D$ (angles in alternate segment are equal)

Also, $∠ D B M = ∠ C B E$ (vertically opposite angles)

Therefore $∠ B A D = ∠ C B E$

Since these are congruent circles, the chord opposite to equal angles are also equal

Therefore BD=CE

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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.

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.