CBSE Class 10 Maths (Basic) 2024 · Paper 430/1/1 · Question 21

Triangles 2 marks Medium

D

is a point on the side

B C

△ A B C

such that

∠ A D C = ∠ B A C

. Show that

A C^{2} = B C \times D C

Triangle ABC with point D on BC and angle ADC = angle BAC

Answer

Since

∠ A D C = ∠ B A C

(given) and

∠ A C D = ∠ B C A

(common),

△ A D C \sim △ B A C

by AA similarity. Hence

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

, so

A C^{2} = B C \times D C

. Hence proved.

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