In a triangle ABC AD is perpendicular to BC such that AB squared is equal to BD into CD prove that ABC is a right triangle right angle at A

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Solution

Given : In triangle ABC , AD is perpendicular to BC and AD² = BD.DC
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

hence proved

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