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If in a triangle, (1-(r(1))/(r(2))) (1 -...

If in a triangle, `(1-(r_(1))/(r_(2))) (1 - (r_(1))/(r_(3))) = 2`, then the triangle is

A

right angled

B

isosceles

C

equilateral

D

none of these

Text Solution

Verified by Experts

We have,
`(1-(s-b)/(s-a))(1-(s-c)/(s-a))=2`
`rArr2(b-a)(c-a)=4(s-a)^(2)`
`rArr2(bc-ac-ab+a^(2)) =(2s -2a)^(2)`
`rArra^(2)=b^(2)+c^(2)`
`rArrDelta` ABC is right angled at A.
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OBJECTIVE RD SHARMA ENGLISH-PROPERTIES OF TRIANGLES AND CIRCLES CONNECTED WITH THEM-Chapter Test
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  2. If the sides of a triangle are in the ratio 3 : 7 : 8, then find R : r

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  9. In a DeltaA B Csum(b+c)tanA/2tan((B-C)/2)=

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  10. In triangle ABC, angleA=pi/3 and b:c =2:3, tan theta=sqrt3/5, 0 lt the...

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  11. In a DeltaABC, AD is the altitude from A. Given b gt c, angleC=23^(@)"...

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  12. If the angles A, B, C (in that order) of triangle ABC are in arithmeti...

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  13. If the radius of the incircle of a triangle withits sides 5k, 6k and 5...

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  15. In a triangleABC, a=13cm, b=12 and c=5cm The distance of A from BC is

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  16. In a triangleABC,B=pi/8, C=(5pi)/(8). The altitude from A to the side ...

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  17. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

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  18. In DeltaABC if a=(b-c)sectheta then (2sqrt(bc))/(b-c)sin(A/2)=

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  19. In a DeltaABC, (a + b + c) (b + c - a) = lambda bc. (where symbols ha...

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  20. If in DeltaABC, a=2b and A=3B, then A is equal to

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  21. Let the angles A , Ba n dC of triangle A B C be in AdotPdot and let b ...

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