The tangent at a point C of a circle and a diameter AB when extended intersect at P. If PCA =
, find
CBA [see Figure].
Solution
Given :
Here [
PC is tangent]
Here OC = OA (Radius)
[
Sides opposite to equal angles are equal]
We know that PC is tangent and angles in alternate segment are equal.
Hence
In
[Interior angles sum of triangle is 180°]
[using (i)]
…..(ii)
Here
( using (ii))
…..(iii)
In
[using (iii)]
Hence