Question

In an acute ABC, AD perpendicular BC, prove that : AC square =AB square +BC square -2BC.BD​

Answer 1

Given:

In ∆ ABC angle B is an acute angle and AD perpendicular BC.

To prove:

AC² =AB² +BC² -2BC.BD

Proof :

In right ∆ADC,

AC² = AD² + CD² [ By pythagoras therome]

=> AC² = AD² + ( BC - BD )² [ DC = BC - BD ]

=> AC² = AD² + BC² + BD² - 2BC.BD

In right ∆ ADB,

AD² + BD² = AB²

=> AC² = AB² + BC² - 2BC.BD

Answer 2

Answer:

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