CBSE Class 10 Maths (Basic) 2025 · Paper 430/2/1 · Question 22

Triangles 2 marks Medium

D

is a point on side

B C

△ A B C

such that

∠ A D C = ∠ B A C

. Prove that

(C A)^{2} = C B \cdot C D

Answer

Since

∠ A D C = ∠ B A C

and

∠ C

is common,

△ A D C \sim △ B A C

(AA). Hence

\frac{C D}{C A} = \frac{C A}{C B}

, so

(C A)^{2} = C B \cdot C D

. Hence proved.

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