# The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA = 110°, find ∠CBA.

Given : A circle with center O in which PC is a tangent a point C and AB is a diameter which is extended to P and PCA = 110°

To Find : CBA

ACB = 90° [Angle in a semicircle is a right angle] [1]

Also,

PCA = ACB + PCB

110 = 90 + PCB

PCB = 20°

Now, PCB = BAC [angle between tangent and the chord equals angle made by the chord in alternate segment]

BAC = 20° [2]

Now In ABC By angle sum property of Triangle.

CBA + BAC + ACB = 180

CBA + 20 + 90 = 180

CBA = 70°

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