Find the ratio of IA:IB:IC, where l is t...

Find the ratio of `IA:IB:IC,` where l is the incentre of `DeltaABC.`

Text Solution

Verified by Experts

The correct Answer is:

`la =r cosec A//2, lb=r cosec B//2, lc =r cosec C//2.`

Topper's Solved these Questions

PROPERTIES AND SOLUTION OF TRIANGLES
ARIHANT MATHS|Exercise Exercise For Sesssion 1|20 Videos
PROPERTIES AND SOLUTION OF TRIANGLES
ARIHANT MATHS|Exercise Exercise For Sesssion 2|19 Videos
PRODUCT OF VECTORS
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos
SEQUENCES AND SERIES
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

The angles of a triangle are in the ratio 3 : 4 : 5. If l be the incentre of DeltaABC then find the measure of angleADC where AD, is the bisector of angleA .

Find the ratio of the circum-radius and the inradius of DeltaABC, whose sides are in the ratio 4:5:6.

The position vectors of the vertices A, B and C of triangle are hati+hatj, hatj+hatk and hati+hatk , respectively. Find the unit vectors hatr lying in the plane of ABC and perpendicular to IA , where I is the incentre of the triangle.

The position vectors of the vertices A,B, and C of a triangle are hat i+hat j,hat j+hat k and hat i+hat k ,respectively.Find the unite vector hat r lying in the plane of ABC and perpendicular to IA, where I is the incentre of the triangle.

In the given figure, ABC is a right angled triangle, right -angled at A in which AB=6 cm, BC=10 cm and I is the incentre of DeltaABC . Find the ara of the shaded region. [Take pi=3.14 ]

Find the distance between the circumcentre and the incentre of the DeltaABC.

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (Questions Asked In Previous 13 Years Exam)

Find the ratio of IA:IB:IC, where l is the incentre of DeltaABC.
Text Solution
|
In a triangle XYZ, let x, y, z be the lengths of sides opposite to the...
Text Solution
|
In a triangle the sum of two sides is x and the product of the same is...
Text Solution
|
Consider a triangle A B C and let a , ba n dc denote the lengths of th...
Text Solution
|
In a triangle PQR, P is the largest angle and cosP=1/3. Further the in...
Text Solution
|
Let PQR be a triangle of area Delta with a = 2, b = 7/2 and c =5/2, wh...
Text Solution
|
If the angle A ,Ba n dC of a triangle are in an arithmetic propression...
Text Solution
|
Let A B C be a triangle such that /A C B=pi/6 and let a , ba n dc deno...
Text Solution
|
a triangle A B C with fixed base B C , the vertex A moves such that co...
Text Solution
|
Let A B Ca n dA B C ' be two non-congruent triangles with sides A B=4,...
Text Solution
|
A straight line through the vertex P of a triangle PQR intersects the ...
Text Solution
|
Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...
Text Solution
|
Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...
Text Solution
|
Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...
Text Solution
|
Internal bisector of /A of triangle ABC meets side BC at D. A line dra...
Text Solution
|
Given an isosceles triangle, whose one angle is-2pi/3 and the radius o...
Text Solution
|
In Delta ABC, which one is true among the following ?
Text Solution
|
Let a vertical tower A b have its end A on the level ground. Let C be ...
Text Solution
|
ABCD is a trapezium such that AB and CD are parallel and BC | CD. If ...
Text Solution
|
For a regular polygon, let r and R be the radii of the inscribed and ...
Text Solution
|
In triangle A B C , let /c=pi/2dot If r is the inradius and R is circu...
Text Solution
|