Grade 99 grade maths
in a triangle ABC , A=90°,CA =AB and D is a point on AB produced. prove that : DC2- BD2=2AB.AD
1 Answer
Arun
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
= { 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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