Question

In triangle ABC, AD triangleBC and AD2
= BD X CD. Prove that
AB2 + AC2 = ( BD + CD) 2.
​

Answer 1

Answer:-

Given:-

• AD triangle BC and AD² = BD × CD

To prove:-

• AB² + AC² = (BD + CD)²

Proof:-

Triangle ADC

$\implies$ (AB)² = (AD)² + BD²------(1)

Triangle ADC

$\implies$ (AC)² = (AD)² + CD²-------(2)

Doing (1) - (2)

AB² - AC² = (AD²+BD²) - (AD²+CD²)

AB² - AC² = AD² + BD² - AD² - CD²

AB² - AC² = BD²-CD²

AB²+CD² = BD²+AC²

AB²+AC² = (BD+CD)²

Hence proved!