Question

in the previous question, what is the distance from a side of the triangle to the incenter? can someone also explain how to get this answer for me?

Answer 1

In centre is the centre of a circle that is inscribed in a triangle, called the incircle, i.e. circle is tangent to all three sides AND located inside the triangle.  An incircle is roughly sketched in the accompanying diagram.

Since all radii of an incircle are equal, we have
4x-1=6x-5
Solving for x,
6x-4x=5-1
x=2
consequently, distance from incentre to each side of the triangle is
4(2)-1=7
check 6x-5=6(2)-5=7... checks.

Answers:
The value of x = 2
The distance from incentre to side of triangle is 7