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In DeltaABC, R, r, r(1), r(2), r(3) deno...

In `DeltaABC, R, r, r_(1), r_(2), r_(3)` denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that `r_(1) :r_(2): r_(3) = 1: 2 : 3`
The value of `R : r` is

A

`5 : 2`

B

`5 : 4`

C

`5 : 3`

D

`3 : 2`

Text Solution

Verified by Experts

The correct Answer is:
A
Area of the triangle, `Delta k^(2) sqrt(11 xx 6 xx 3 xx 2) = 6 sqrt11 k^(2)`
So, `r = (Delta)/(s) = (6)/(sqrt11) k`
And, `R = (abc)/(4Delta) = (5 xx 8 xx 9)/(4 xx 6 xx sqrt11) k = (15)/(sqrt11) k`
`:. R : r = 5 : 2`
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  6. Internal bisectors of DeltaABC meet the circumcircle at point D, E, an...

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  8. The area of any cyclic quadrilateral ABCD is given by A^(2) = (s -a) (...

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  9. The area of any cyclic quadrilateral ABCD is given by A^(2) = (s -a) (...

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  10. The area of any cyclic quadrilateral ABCD is given by A^(2) = (s -a) (...

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  11. In DeltaABC, R, r, r(1), r(2), r(3) denote the circumradius, inradius,...

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  12. In DeltaABC, R, r, r(1), r(2), r(3) denote the circumradius, inradius,...

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  15. In DeltaABC, P,Q, R are the feet of angle bisectors from the vertices ...

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  18. Let G be the centroid of triangle ABC and the circumcircle of triangle...

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