What is raduis R of a circle inscribed into a triangle?

Question

The circle which is tangent
to side a and extensions b and c has raduis Ra = 3
to side b and extensions a and c has raduis Rb = 4
to side c and extensions a and b has raduis Rc = 6

Answer 1

we have the relation:

1/Ra + 1/Rb + 1/Rc = 1/R; where R is the inradius of the given triangle. [inradius = radius of the circle inscribed in a triangle]. i.e.
1/3 + 1/4 + 1/5 = 1/R or R = 1.2771 correct to 4 decimal places.

Answer 2

Good question.

The inradius of a triangle is given by r = A/s, where
A= area of triangle and s= semiperimeter of triangle.

The problem is how to relate the sides of the triangle to the three given radii. I am still trying to uncoverthat relationship.

Answer 3

r1=3 area/s-a=3
r2=4 area/s-b=4
r3=6 area/s-c=6

r=area/s s=(a+b+c)/2
use above equations

Answer 4

What are u asking for?

Answer 5

1.27