In Fig. 6.59, ABC is a triangle in which &ang; ABC

Question

In Fig. 6.59, ABC is a triangle in which &ang; ABC < 90&deg; and AD &perp; BC. Prove that

Philoid · Accepted Answer

Applying Pythagoras theorem in ΔADB, we obtain

AD² + DB² = AB²

AD² = AB²– DB² (i)

Applying Pythagoras theorem in ΔADC, we obtain

AD² + DC² = AC²

AB²– BD² + DC² = AC² [Using equation (i)]

AB²– BD² + (BC - BD)² = AC²

AC² = AB²– BD² + BC² + BD² -2BC x BD

= AB² + BC² - 2BC x BD