The diameter of the inscribed circle in the triangle is 42 units
How to find the diameter
This incircle, entirely enclosed by the triangle, is the largest possible circle that doesn't extend beyond the triangle's boundaries.
The segments labeled with lengths x + 8 and 2x - 5 represent two radii of the incircle, touching the sides of the triangle.
Setting these expressions equal due to the equality of all radii, we solve for x.
x + 8 = 2x - 5
8 + 5 = 2x - x
13 = x
We find the length of one radius
13 + 8 = 21
diameter = 2 * radius = 2 * 21 = 42
Complete question
What is the diameter of the inscribed circle of the triangle?
The diameter of the inscribed circle of the triangle is _____