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D is a point on the side BC of triangle ABC such that angle ADC is equal to angle BAC. Prove that: CA2 = CB x CD.

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In ΔADC and ΔBAC,

D is a point on the side BC of triangle ABC such that angle ADC is equal to angle BAC. Prove that: CA^2 = CB x CD. Similarity, Concise Mathematics Solutions ICSE Class 10.

⇒ ∠ADC = ∠BAC [Given]

⇒ ∠ACD = ∠ACB [Common]

∴ ∆ADC ~ ∆BAC [By AA]

Since, corresponding sides of similar triangles are proportional we have :

⇒ CACB=CDCA\dfrac{CA}{CB} = \dfrac{CD}{CA}

⇒ CA2 = CB x CD.

Hence, proved that CA2 = CB x CD.

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