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Q.

If r:R:r1=2:5:12 then prove that the triangle is right angled at A.

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answer is 1.

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Detailed Solution

Given r:R:r1=2:5:12 r2=R5=r112=k

r=2k,R=5k,r1=12k

r1r=12k2k=10k=2(5k)=2R

r1r=2R

4RsinA2cosB2cosC2sinB2sinC2=2R

r1=4RsinA2cosB2cosC2,r=4RsinA2sinB2sinC2

4RsinA2cosB+C2=2R2sin2A2=1

sin2A2=12sinA2=12

A2=450A=900

 The triangle is right angled at ‘A’.

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