Question

In a circle with centre P, AB and CD are congruent chords. If angle PAB= 40 degrees, then find angle CPD. The answer should be 100 degrees

Answer 1

Given: A circle with Center P, such that AB and CD are congruent chords.

    Also, ∠P AB = 40°,

To Find: ∠CPD=?

Solution:

In the circle , with center P

∠P AB=40°

PA=PB→→Radii of Circle

∠PA B= ∠P A B=40°→→ if in a triangle , opposite sides are equal angle opposite to them are equal.

∠AP B + ∠PA B + ∠P B A= 180°→→Angle Sum Property of triangle

40° +40°+∠APB=180°

∠APB=180° - 80°

∠APB=100°

In ΔAPB and ΔP CD

$\frac{AP}{PD}=\frac{BP}{PC}=\frac{AB}{CD}=1$  

ΔAPB ~ ΔP CD→→[SSS]

∠APB=∠CPD=100°→→→[By Similarity Criterion]

∠CPD=100°

Hence Proved.