P is a point on the side BC of ABC such that ∠ APC = ∠ BAC . Prove that AC2 = BC · CP .

CBSE Class 10 Maths PYQ · Triangles · Similarity with Triangles · 2 Marks · March 2025 · Standard

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922 Marks · March 2025 · Standard

$P$ is a point on the side $BC$ of $\Delta ABC$ such that $\angle APC = \angle BAC$. Prove that $AC^2 = BC \cdot CP$.

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Correct figure ($\frac{1}{2}$ mark). $\angle APC = \angle BAC$, $\angle ACP = \angle ACB$ (1 mark). $\therefore \Delta APC \sim \Delta BAC$. $AC^2 = BC \cdot CP$ ($\frac{1}{2}$ mark).