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In the figure (ii) given below, ∠ADC = ∠BAC. Prove that CA2 = DC × BC.

In the figure (ii) given below, ∠ADC = ∠BAC. Prove that CA2 = DC × BC. Similarity, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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ICSE

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Answer

In △ABC and △ADC

∠C = ∠C (Common angle for both triangle)

∠BAC = ∠ADC (Given)

Then, by AA rule of similarity, △BAC ~ △ADC.

So,

CADC=BCCACA2=DC×BC.\dfrac{CA}{DC} = \dfrac{BC}{CA} \\[1em] CA^2 = DC \times BC.

Hence proved.

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