Question

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?

• A. $x>y$
• B. $x<y$
• C. $x=y$
• D. $x+y={90}^{\circ }$

Answer 1

The correct option is C

$x=y$

Join the points OP,OA and OB
Now, in triangles OPA and OPB,
OP = OP (common side)
OA = OB (radii)
$\angle OAP=\angle OBP={90}^{\circ }$ (Tangent is perpendicular to the radius)
Hence, $\Delta OAP\cong \Delta OBP$ (RHS congruency)
Hence, $\angle OPA=\angle OPB$ (CPCT)
Or, x = y.