Q. 124.7( 18 Votes )

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

Answer :


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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