In the figure given below, PA and PB are tangents to the circle from point P. When the centre of the circle O and the point P are joined, how are the values of x and y related?
x=y
Join the points OP, OA and OB
Now, in triangles OPA and OPB,
OP = OP (common side)
OA = OB (radii)
∠OAP=∠OBP=90∘ [Tangent is perpendicular to the radius]
Hence, △OAP≅△OBP [RHS congruency]
Hence, ∠OPA=∠OPB [CPCT]
Or, x=y.