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If two sides of a triangle are roots of the equation `x^(2) -7x + 8 = 0` and the angle between these sides is `60^(@)` then the product of inradius an

Monjur Alahi

If two sides of a triangle are roots of the equation `x^(2) -7x + 8 = 0` and the angle between these sides is `60^(@)` then the product of inradius and circumradius of the triangle is
A. `(8)/(7)`
B. `(5)/(3)`
C. `(5sqrt2)/(3)`
D. 8


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Salim Ahmed Kawsar

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Correct Answer - B
Let a and b the roots of `x^(2) -7 x + 8 = 0`
Then `a + b = 7, ab = 8`
Also, `C = 60^(@)`
`rArr c^(2) = a^(2) + b^(2) - ab`
`rArr c^(2) = (a +b)^(2) -3ab = 49 -24 = 25`
`rArr c = 5`
`:. r.R = (abc)/(2(a+b+c)) = (8xx5)/(2(7+5)) = (5)/(3)`

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