If D is a point on the side BC of a triangle ABC such that ∠ADC=∠BAC then, CA2 = _____.
A
BC.CD
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B
BD.DC
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C
BC.BC
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D
AD.DC
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Solution
The correct option is A BC.CD Given: ∠ADC=∠BAC In △BAC and △ADC, ∠ACB=∠ACD .... (common angles) ∠BAC=∠ADC .... (Given) ∴△BAC∼△ADC .... (AA simlilarity) ⇒BAAD=ACCD=BCAC⇒ACCD=BCAC⇒AC2=BC.CD