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Let G be the centroid of triangle ABC an...

Let G be the centroid of triangle ABC and the circumcircle of triangle AGC touches the side AB at A
If `BC = 6, AC = 8`, then the length of side AB is equal to

A

`(1)/(2)`

B

`(2)/(sqrt3)`

C

`5sqrt2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C

`FG xx FC = FA^(2)`
`rArr (1)/(3) (FC^(2)) = FA^(2)`
`rArr (2a^(2) + 2b^(2) -c^(2))/(3 xx4) = (c^(2))/(4)` (Using Apollonious theorem)
`rArr 2c^(2) = a^(2) + b^(2)`
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CENGAGE PUBLICATION-PROPERTIES AND SOLUTIONS OF TRIANGLE-Linked comprehension type
  1. An isosceles triangle has two equal sides of length 'a' and angle betw...

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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. Bisectors of angles A, B and C of a triangle ABC intersect its circum...

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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 triangleABC, P,Q, R are the feet of angle bisectors from the vertic...

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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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