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If the sides of triangle are in the rati...

If the sides of triangle are in the ratio `3 : 5 : 7`, then prove that the minimum distance of the circumcentre from the side of triangle is half the circmradius

Text Solution

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We have `a : b : c = 3 : 5 : 7`
Distance of circumcentre from sides are `R |cos A|, R| cos B| and R|cos C|`.
So, `R|cos C|` is minimum
`cos C = (3^(2) + 5^(2) -7^(2))/(2 xx 3 xx 5) = (9 + 25 - 49)/(30) = (-1)/(2)`
so, required minimum distance is `R//2`
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