In triangle ABC, `R (b + c) = a sqrt(bc)`, where R is the circumradius of the triangle. Then the triangle is

Monjur Alahi

In triangle ABC, `R (b + c) = a sqrt(bc)`, where R is the circumradius of the triangle. Then the triangle is
A. isosceles but not right
B. right but not isosceles
C. right isosceles
D. equilateral


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Salim Ahmed Kawsar

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Correct Answer - C
`R(b +c) = a sqrt(bc) = 2R sin A sqrt(bc)`
`:. sin A = (b +c)/(2sqrt(bc))`
Now `sin A le 1`
`rArr (b + c)/(2sqrt(bc)) le 1`
or `(sqrtb - sqrtc)^(2) le 0`
or `b = c`
`rArr sin A = 1`
`rArr A = 90^(@) and b = c`
Hence, the triangle is right isosceles.

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