Question

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

AC2= AB2+ BC2+ 2 BC.BD.

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Answer 1

Given :-

• ABC is a triangle.
• ∠ABC > 90°
• AD ⊥ CB

To Prove :-

• AC² = AB² + BC² + 2 BC.BD.

Proof :-

By applying Pythagoras Theorem in ∆ADB, we get,

=> AB² = AD² + DB² ……………………… (i)

Again, by applying Pythagoras Theorem in ∆ACD, we get,

=> AC² = AD² + DC²

=> AC² = AD² + (DB + BC)²

=> AC² = AD² + DB² + BC² + 2DB × BC

From equation (i), we can write,

=>AC² = AB² + BC² + 2DB × BC

Hence, proved !!!