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प्रश्न
In triangle ABC point D is on side BC (B-D-C) such that ∠BAC = ∠ADC then prove that CA2 = CB × CD
सिद्धांत
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उत्तर
Proof:
In ΔBAC and ΔADC,
∠BAC ≅ ∠ADC ...[Given]
∠BCA ≅ ∠ACD ...[Common angle]
∴ ΔBAC ∼ ΔADC ...[AA test of similarity]
∴ `(CA)/(CD) = (CB)/(CA)` ...[Corresponding sides of similar triangles]
∴ CA × CA = CB × CD
∴ CA2 = CB × CD
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