Question

Two congruent circles intersect each other at points A and B. Through A any line segment PAQ is drawn so that P, Q lie on the two circles. Prove that BP = BQ.

Answer 1

Data : Two congruent circles intersect each other at points A and B. 

Through A any line segment PAQ is drawn so that P, Q lie on the two circles. 

To Prove: BP = BQ 

Construction: Join AB. 

Proof: Two congruent triangles with centres O and O’ intersects at A and B. Through A segment PAQ is drawn so that P, Q lie on the two circles. 

Similarly, ∠AQB= 70° in circle subtended by chord AB. Because Angles subtended by circumference by same chord. 

∴ ∠APB = ∠AQB = 70°. 

Now, in ∆PBQ, ∠QPB = ∠PQB. 

∴ Sides opposite to each other are equal. 

∴ BP = BQ.