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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 greatest angle of the triangle is given by

A

`cos^(-1) ((1)/(30))`

B

`cos^(-1)((1)/(3))`

C

`cos^(-1)((1)/(10))`

D

`cos^(-1) ((1)/(5))`

Text Solution

Verified by Experts

The correct Answer is:
C
Since c is the greatest side, C is the greatest angle
`cos C = (a^(2) + b^(2) -c^(2))/(2ab) = (25 + 64 - 81)/(2 xx 5 xx 8) = (1)/(10)`
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CENGAGE-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercise (Comprehension)
  1. Given an isoceles triangle with equal side of length b and angle alpha...

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  2. Incircle of DeltaABC touches the sides BC, AC and AB at D, E and F, re...

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  3. Incircle of DeltaABC touches the sides BC, AC and AB at D, E and F, re...

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  4. Incircle of DeltaABC touches the sides BC, AC and AB at D, E and F, re...

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  5. Internal bisectors of DeltaABC meet the circumcircle at point D, E, an...

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  6. Internal bisectors of DeltaABC meet the circumcircle at point D, E, an...

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

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

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

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

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

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

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  19. The inradius in a right angled triangle with integer sides is r If r...

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  20. The inradius in a right angled triangle with integer sides is r If r...

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