In Fig. 6.58, ABC is a triangle in which ∠ ABC > 90° and AD ⊥ CB produced. Prove that

Question

In Fig. 6.58, ABC is a triangle in which &ang; ABC > 90&deg; and AD &perp; CB produced. Prove that

Philoid · Accepted Answer

Using Pythagoras theorem in ΔADB, we get:

AB² = AD² + DB² (i)

Applying Pythagoras theorem in ΔACD, we obtain

AC² = AD² + DC²

AC² = AD² + (DB + BC)²

AC² = AD² + DB² + BC² + 2DB x BC

AC² = AB² + BC²+ 2DB x BC [Using equation (i)]