Question

If the incircle of the triangle abc touches its sides respectively at l,m and n and if x,y,z be the circumradii of the triangles min,nil and lim where i is the incentre then the product xyz is

Answer 1

Answer:

In figure ANIM is a cyclic quadrilateral

Also AI is the diameter of circumcircle MNI.

Let AI=2x

Then cosec

2

A

=

r

2x

⇒x=

2sin

2

A

r

,y=

2sin

2

B

r

,z=

2sin

2

C

r

⇒xyz=

8sin

2

A

sin

2

B

sin

2

C

r

3

=

2

R

r

r

3

=

2

r

2

R

Step-by-step explanation:

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