CBSE Class 10 Maths (Standard) 2019 · Paper 30/4/2 · Question 26

Triangles 4 marks Medium

△ A B C

(Figure 3),

A D ⊥ B C

. Prove that

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

Triangle ABC with altitude AD perpendicular to BC

Answer

Proved:

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

, using the Pythagoras theorem on triangles

A D C

and

A D B

with

D C = B C - B D

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