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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 5 · Set 1 · Q22
In the given figure, PT is a tangent to the circle centered at O. OC is perpendicular to chord AB. Prove that PA. PB = PC^2- AC^2.
In the given figure, PT is a tangent to the circle centered at O. OC is perpendicular to chord AB. Prove that PA . $\displaystyle \mathrm{PB}=\mathrm{PC}^{2}-\mathrm{AC}^{2}$.
Marking-scheme solution
\[\begin{aligned}
& \mathbf{P A} \cdot \mathbf{P B}=(\mathbf{P C}-\mathbf{A C}) \cdot(\mathbf{P C}+\mathbf{B C}) \\
& =(\mathbf{P C}-\mathbf{A C})(\mathbf{P C}+\mathbf{A C}) \quad[\mathbf{A C}=\mathbf{B C}] \\
& =\mathbf{P C}^{2}-\mathbf{A C}^{2}
\end{aligned}
\]
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.