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If the distance between incenter and one...

If the distance between incenter and one of the excenter of an equilateral triangle is 4 units, then find the inradius of the triangle.

Text Solution

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Distance between excenter `I_(1) and` incenter I is
`II_(1) = 4R sin.(A)/(2) = 4` (given)
Since triangle, we have
`4 = 4R sin.(pi)/(6)`
or `R = 2`
`:. R = 2r = 2`
or `r = 1`
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