Question

anybody plz help me in this two problems

Answer 1

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We know, △ADB∼△ABC

Therefore, AD.AB=AB.AC (Condition for similarity)

Or, AB²=AD×AC……..(1)

Also, △BDC∼△ABC

Therefore, CD.BC=BC.AC (Condition for similarity)

Or, BC²=CD×AC……..(2)

Adding the equations (1) and (2) we get,

AB²+BC² = AD×AC+CD×AC

AB²+BC² = AC(AD+CD)

Since, AD + CD = AC

Hence, AC² = AB² + BC²


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