Question

ABC is a triangle in which angle ABC is greater than 90 degree and AD is perpendicular on CD produced. Prove that AC square is equals to AB square + BC square + 2 BC. BD

Answer 1

The answer is attached

Answer 2

ABC is a triangle in which angle ABC is greater than 90 degree and AD is perpendicular on CD produces. It is to Prove that AC square is equal to AB square + BC square +2 BC.BD. The step wise explanation is given below :

- It is giventhat in ΔABC

∠ ABC > 90°

AD ⊥ CD

- We need to prove that-

AC² = AB² + BC² + 2 BC·BD

- So,

In Δ ADB,

AB² = AD² + BD² ........(1)

In Δ ADC,

AC² = AD² + CD² ........(2)

AC² = AD² + (BD+BC)²            (CD = BD+BC)

- By using the formula [(a+b)²=a²+b²+2ab]

AC² = AD² + BD² + BC² + 2BD·BC

AC² = (AD² + BD²) + BC² + 2BD·BC

- From (1), we get

AC² = AB² + BC² + 2BD·BC

Hence proved