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In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC^2 = AB^2 + BC^2 + 2BC.BD. - Mathematics

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

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Solution

Applying Pythagoras theorem in ΔADB, we obtain

AB2 = AD2 + DB2 … (1)

Applying Pythagoras theorem in ΔACD, we obtain

AC2 = AD+ DC2

AC2 = AD2 + (DB + BC)2

AC2 = AD2 + DB2 + BC2 + 2DB × BC

AC2 = AB2 + BC2 + 2DB × BC [Using equation (1)]

Concept: Pythagoras Theorem
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APPEARS IN

NCERT Class 10 Maths
Chapter 6 Triangles
Exercise 6.6 | Q 3 | Page 152
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