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In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD. - Mathematics

In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.

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Solution

Applying Pythagoras theorem in ΔADB, we obtain

AD2 + DB2 = AB2

⇒ AD2 = AB2 − DB2 … (1)

Applying Pythagoras theorem in ΔADC, we obtain

AD2 + DC2 = AC2

AB2 − BD2 + DC2 = AC2 [Using equation (1)]

AB2 − BD2 + (BC − BD)2 = AC2

AC2 = AB2 − BD2 + BC2 + BD2 −2BC × BD

= AB2 + BC2 − 2BC × BD

Concept: Pythagoras Theorem
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APPEARS IN

NCERT Class 10 Maths
Chapter 6 Triangles
Exercise 6.6 | Q 4 | Page 152
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