Question

31. ABC
Prove
is a
that
triangle ADI BC and BD = 3 CD.
2 (AB) ² = 2(A) ² + BC ².​

Answer 1

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Answer 2

In right triangles ∆ADB and ∆ADC

So, Pythagoras theorem should be applied,

Then we have ,

AB² = AD² + BD² ______(1)

AC²= AD²+ DC² ______(2)

AB² + AC² = 2AD² + BD²+ DC²

= 2BD . CD + BD² + CD² [ ∵ given AD² = BD.CD ]

= (BD + CD )² = BC²

Thus in triangle ABC we have , AB² + AC²= BC²

Hence triangle ABC is a right triangle right angled at A

∠ BAC = 90°