Question

in a circle with centre P, AB and CD are congruent chords. If angle PAB= 40 degrees, then find angle CPD

Quick please

Answer 1

acorrding to theorem 10.8

Answer 2

Answer:

∠CPD = 100°

Step-by-step explanation:

Given: AB and CD are congruent chords

          ∠PAB = 40°

To find: ∠CPD

In ΔAPB

AP = PB (radii of a circle)

⇒ ∠PAB = ∠PBA = 40° (angles opposite to equal sides are equal)

∠PAB + ∠PBA + ∠APB = 180° (Angle Sum Property)

40 + 40 + ∠APB = 180

∠APB = 180 - 80

∠APB = 100°

AB = CD

⇒ ∠CPD = ∠APB = 100° (Equal angles subtended by equal chords)

Therefore, ∠CPD = 100°