CBSE Class 10 Maths (Basic) 2020 · Paper 430/1/1 · Question 38(b)

Triangles 4 marks Medium

In an obtuse

△ A B C

(

∠ B

is obtuse),

A D

is perpendicular to

C B

produced. Then prove that

A C^{2} = A B^{2} + B C^{2} + 2 B C \times B D

Answer

Using Pythagoras in

△ A D C

and

△ A D B

with

D C = B C + B D

gives

A C^{2} = A B^{2} + B C^{2} + 2 B C \times B D

; hence proved.

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