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Mathematics · 2024 · 3 marks
CBSE 2024 · Region 3 · Set 3 · Q30
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.
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.
Marking-scheme solution
\[\begin{gathered}
\triangle \mathrm{ACP} \cong \triangle \mathrm{BCP} \\
\mathrm{AC}=\mathrm{BC} \\
\angle \mathrm{ACP}=\angle \mathrm{BCP} \\
\mathrm{CP}+\angle \mathrm{BCP}=180^{\circ} \\
\angle \mathrm{ACP}=90^{\circ}
\end{gathered}
\]
\(\displaystyle \Rightarrow \mathrm{OP} \perp \mathrm{AB}\)
Hence OP is perpendicular bisector of chord AB .More from Circles
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CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.