From an external point P, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the…

CBSE Class 10 Maths PYQ · Circles · Triangle & Circle · 3 Marks · March 2024 · Standard

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943 Marks · March 2024 · Standard

From an external point P, two tangents PA and PB are drawn to the circle with centre O. Prove that OP is the perpendicular bisector of chord AB.

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Sol.
Correct Fig.
$\triangle$ACP $\cong \triangle$BCP
AC=BC
$\angle$ACP = $\angle$BCP
$\angle$ACP + $\angle$BCP = $180^{\circ}$
$\angle$ACP = $90^{\circ}$
$\Rightarrow$ OP $\perp$ AB
Hence OP is perpendicular bisector of chord AB.