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?

$P A > P B$

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$P A < P B$

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$P A = P B$

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$P A^{2} = P B^{2} + r^{2}$

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Solution

The correct option is C
$P A = P B$

Join the points OP, OA and OB
Now, in triangles OPA and OPB,
OP = OP (common side)
OA = OB (radii)
$∠ O A P = ∠ O B P = 90^{\circ}$ [Tangent is perpendicular to the radius]
Hence, $△ O A P ≅ △ O B P$ [RHS congruency]
Hence, PA = PB [CPCT]

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