Question

AB is the diameter of the circle such that anglePAB = 40°. Find angle PCA and angle POB

Answer 1

I hope this will help you!!!!!!!!

Answer 2

∠POB =  80°  & ∠PCA = 50°  

Step-by-step explanation:

AB is the diameter of the circle

∠PAB = 40°

∠POB = 2 ∠PAB  ( Angle subtended by chord PB at center = 2 at arc segment)

=> ∠POB =  2* 40°

=> ∠POB =  80°

AB is a diameter Hence O lies on AB

=> ∠POA + ∠POB = 180°

=> ∠POA + 80° = 180°

=> ∠POA  = 100°

∠POA =  2 ∠PCA  ( angle subtended by chord PA)

=> 100°  =  2 ∠PCA

=> ∠PCA = 50°  

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