In the given figure, PT is a tangent to the circle centered at O . OC is perpendicular to chord AB . Prove that PA ·…

CBSE Class 10 Maths PYQ · Circles · Triangle & Circle · 2 Marks · March 2023 · Standard

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852 Marks · March 2023 · Standard

In the given figure, $PT$ is a tangent to the circle centered at $O$. $OC$ is perpendicular to chord $AB$. Prove that $PA \cdot PB = PC^2 - AC^2$.

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$PA \cdot PB = (PC - AC) \cdot (PC + BC)$
$= (PC - AC) \cdot (PC + AC)$
quad $[AC = BC]$
$= PC^2 - AC^2$