Question

In the figure given below, PA and PB are tangents to the circle from point P. Which of the following is the correct relation between PA and PB?

• A. $PA>PB$
• B. $PA<PB$
• C. $PA=PB$
• D. $P{A}^2=P{B}^2+r^2$

Answer 1

The correct option is C $PA=PB$



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, PA = PB (CPCT)