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in a triangle ABC , A=90°,CA =AB and D is a point on AB produced. prove that : DC2- BD2=2AB.AD

in a triangle ABC , A=90°,CA =AB and D is a point on AB produced. prove that : DC2- BD2=2AB.AD

Grade:9

1 Answers

Arun
25763 Points
3 years ago
DC^2 = (AC^2 + AD^2) 
= { AB^2 + (AB + BD)^2} 
= { AB^2 + AB^2 + BD^2 + 2 AB*AD } 
= { 2AB^2 + 2 AB*AD } + BD^2 
= { 2AB (AB + AD) } + BD^2 
= { 2 AB * AD } + BD^2 
or, DC^2 = 2AB*AD + BD^2 
or, DC^2 - BD^2 = 2AB*AD

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