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Q.

In an equilateral triangle, the inradius, circumradius and one of the ex-radii are in the ratio

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a

2:3:5 

b

1:2:3 

c

1 :3:7

d

3:7:9

answer is B.

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Detailed Solution

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we have Δ=34a2,s=3a2
 r=Δs=a23,R=abc4Δ=a33a2=a3 and r1=Δsa=3/4a2a/2=32a
 Hence, r:R:r1=a23:a3:32a=1:2:3

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In an equilateral triangle, the inradius, circumradius and one of the ex-radii are in the ratio