InterviewSolution
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InterviewSolution
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In ∆ABC if AB = AC and a point D lies of AC such that BC2 = AC × DC, then Prove that BD = BC. |
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Answer» Given : In ∆ABC, AB = AC and BC2 = AC × DC, where D is any point on side AC. To prove : BD = BC Proof : Given that BC2 = AC × DC ⇒ BC/DC = AC/BC …..(i) Now in ∆ABC and ∆BDC ∠C = ∠C (common angle) and BC/DC = AC/BC [from (i)] Thus, by SAS similarity criterion ∆ABC ~ ∆BDC ⇒ AC/BC = AB/BD …..(ii) Given, AB = AC Thus, AC/BC = AC/BD ⇒ BC = BD. |
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