Question

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Answer 1

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Answer 2

Heya Dear 

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Question : In a ΔABC ,  AD⊥BC and AD² = BD x CD , prove that ΔABC is right angled triangle .

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Solution : 

Given : In triangle ABC , AD is perpendicular to BC and AD² =  BD x CD 

To prove : BAC = 90°

Proof : In right triangles ADB and ADC 

we have , AB² = AD² + BD² ______(1)

 and         AC² = AD² + DC² ______(2)

From (1) and (2) , we get 

AB² + AC² = 2AD² x BD² + DC² 

AB² + AC² = 2BD  x CD + BD² + CD²  { AD² = BD x CD ( given) } 

AB² + AC² = (BD + CD)² 

AB² + AC² = BC² 

Hence triangle ABC is a triangle right angled at  A . 

BAC = 90° 

Hence proved 

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