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Question

In In ΔABC, if 8R2=a2+b2+c2, then the triangle is


A

Right angled

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B

Equilateral

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C

Acute angled

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D

Obtuse angled

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Solution

The correct option is A

Right angled


8R2=a2+b2+c2=4R2(sin2A+sin2B+sin2C)sin2A+sin2B+sin2C=2(cos2Asin2C)+cos2B=0cos(AC)cos(A+C)+cos2B=0cos(AC)cos(A+C)+cos2(π(A+C))=0cos(A+C)(cos(AC)+cos(A+C))=0cos(πB)(2cosAcosC)=02cosAcosCcosB=0
cosA=0 or cosB=0 or cosC=0a=π2 or B=π2 or C=π2


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