Question

In triangle ABC, AD is perpendicular to BC, AD^2=BD×CD. Prove that triangle is a right triangle.

Answer 1

Proof:-

In right angled triangles ADB and ADC

BD^2+AD^2=AB^2………….(1)

DC^2++AD^2=AC^2………..(2)

On adding eq.(1) & (2)

BD^2+DC^2+2AD^2=AB^2+AC^2

Put AD^2=BD.DC (given)

BD^2+DC^2+2BD.DC=AB^2+AC^2

(BD+DC)^2=AB^+AC^2 , put BD+DC=BC

BC^2=AB^2+AC^2 , therefore in triangle ABC

BC is hypotenues and angle BAC=90° , Proved.

Answer 2

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