Question

in right angle triangle ABC C is 90degree and D is theid point of BC prove that BC square =4(AD square-ac square) ​

Answer 1

In ∆ ABC :-

=> AC² = AB² + BC² -------- (1)

and, in ∆ ABD :-

=> AD² = AB² + BD²

=> AB² = AD² - BD² --------- (2)

=> BD² = AD² - AB² --------- (3)

Taking equation - (1) :-

=> AC² = AB² + BC²

=> AC² = AD² - BD² + BC² --{from - (2)}

=> AC² = AD² - BD² + (BD + DC)²

=> AC² = AD² - BD² + BD² + DC² + 2BD.DC

=> AC² = AD² + DC² + 2BD.DC

=> AC² = AD² + DC² + 2BD.BD

=> AC² = AD² + BD² + 2BD²

=> AC² = AD² + 3BD²

=> AC² = AD² + 3(AD² - AB²) ----{from - (3)}

=> AC² = AD² + 3AD² - 3AB²

=> AC² = 4AD² - 3AB²

Q.E.D.