Ex 6.3, 13 - D is a point on side BC of a triangle ABC - AA Similarity

  1. Class 10
  2. Important Questions for Exam - Class 10
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Ex 6.3, 13 D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC. Show that CA2 = CB.CD Given: ΔABC where ∠ ADC = ∠ BAC To Prove: CA2 = CB.CD i.e. 𝐶𝐴/𝐶𝐷 = 𝐶𝐵/𝐶𝐴 Proof:- In ∆ BAC and ∆ ADC ∠ACB = ∠ACD ∠BAC = ∠ADC Hence by AA similarity criterion ∆ BAC ∼ ∆ ADC ∆ BAC ∼ ∆ ADC Hence 𝐵𝐴/𝐴𝐷=𝐴𝐶/𝐶𝐷=𝐵𝐶/𝐴𝐶 Hence 𝐴𝐶/𝐶𝐷=𝐵𝐶/𝐴𝐶 AC2 = BC . CD Hence proved

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