Question

in triangle abc a= 90 ab=ca and d is a point in ab produced
prove ; dc^2-bd^2=2ab*ad

Answer 1

 In a triangle ABC,∠A = 90°, CA=AB and D is a point on AB produced. According to Pythagoras theorem, DC2 = AD2 + AC2 DC² - BD² = (AD2 + AC2) - (AD - AB)2= (AD2 + AC2) - (AD2 + AB2 - 2 AD . AB) =  AD2 + AC2 - AD2 - AB2 + 2 AD . AB = AC2 - AB2 + 2 AD . AB= AC2 - AC2 + 2 AD . AB [Since AC = AB] = 2 AD . ABHence proved.

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Answer 2

Answer:

Step-by-step explanation:

In ACD

A=90

H^2= B^2+P^2

DC^2=AD^2+AC^2

DC^2=AC^2+[AB+BD] ^2

DC^2=AC^2+AB^2+BD^2+2AB.BD

DC^2-BD^2=AC^2+AB^2+2AB.BD

DC^2-BD^2=AB^2+AB^2+2AB.AD [SINCE AC=AB]

DC^2-BD^2=2AB[AB+BD]

DC^2-BD^2=2AB.AD [SINCE AB+BD=AD]

H. P