Home
Class 11
MATHS
value of the expression (b-c)/(r(1))+(c-...

value of the expression `(b-c)/(r_(1))+(c-a)/r_(2)+(a-b)/r_(3)` is equal to

A

1

B

2

C

3

D

0

Text Solution

Verified by Experts

`((b-c))/(r_(1))+((c-a))/r_(2)+((a-b))/r_(3)`
`rArr (b-c)((s-a)/(Delta))+(c-a)((s-b)/(Delta))+(a-b)((s-c)/(Delta))`
`rArr ((s-a)(b-c)+(s-b)(c-a)+(s-c)(a-b)])/(Delta)=(0)/(Delta)=0`
Thus , `(b-c)/r_(1)+(c-a)/r_(2)+(a-b)/r_(3)=0`
Promotional Banner

Topper's Solved these Questions

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise Illustration|27 Videos

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise EXERCISE-I|29 Videos

  • SOLUTION AND PROPERTIES OF TRIANGLE

    ALLEN|Exercise All Questions|62 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    ALLEN|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

The value of (b-c)/(r_(1))+(c-a)/(r_(2))+(a-b)/(r_(3)) is equal to

Show that (b-c)/(r _(1))+ (c-a)/(r _(2))+(a-b)/(r _(3)) =0.

The value of expression (C_(1))/(2)+(C_(3))/(4)+(C_(5))/(6)+.... is equal to (where C_(r)=^(n)C_(r) )

If r_(1), r_(2) ,r_(3) are the ex-radii of DeltaABC, then prove that (bc)/(r_(1))+(ca)/(r _(2))+(ab)/(r _(3))=2R [((a)/(b)+(b)/a)+((b)/(c)+(c)/(b))+((c)/(a)+ (a)/(c))-3]

O is the circumcentre of the triangle ABC and R_(1),R_(2),R_(3) are the radii of the circumcirclesof the triangles OBC,OCA and OAB respectively,then (a)/(R_(1))+(b)/(R_(2))+(c)/(R_(3)), is equal to

In triangleABC , If r_(1), r_(2), r_(3) are exradii opposites to angles A,B and C respectively. Then (1/r_(1) +1/r_(2)) (1/r_(2)+1/r_(3)) (1/r_(3)+1/r_(1)) is equal to

In triangle ABC, if r_(1)=3r, then the value of tan((A)/(2))(tan((B)/(2))+tan((C)/(2))) is equal to

If a,b,c denote the sides of triangleABC , show that the value of the expression, a^3 (p-q)(p-r)+b^2(q-r)+b^2(q-r)(q-p)+c^2(r-p)(r-q) cannot be negative where p,q,r in R .

Prove that (r_(1) -r)/(a) + (r_(2) -r)/(b) = (c)/(r_(3))

In any triangle,the minimum value of r_(1)r_(2)r_(3)/r^(3) is equal to 1(b)9(c)27(d) none of these