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प्रश्न
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.
उत्तर
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
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