Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.
Here PQ and PR are tangents and O is the center of the circle.
Let us join OQ and OR.
Here
( tangent from exterior point is perpendicular to the radius through the point of contact)
In PQO andPRO
(Radius of circle)
(Common side)
Hence, [RHS interior]
Hence, [By CPCT]
Hence O lies on the angle bisector of
Hence Proved.