Triangle \(\triangle ABC\) has a right angle at C, A = 60 degrees, and AC = 10. Find the radius of the incircle of \(\triangle{ABC}\).

supremecheetah May 23, 2023

#1**0 **

Right scalene triangle.

Sides: a = 20 b = 17.321 c = 10

Area: T = 86.603

Perimeter: p = 47.321

Semi-perimeter: s = 23.66

Angle ∠ A = α = 90° = 1.571 rad

Angle ∠ B = β = 60° = 1.047 rad

Angle ∠ C = γ = 30° = 0.524 rad

Inradius

An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.

**Inradius ==Area / semi-perimeter ==86.603 / 23.66 ==3.66**

Guest May 23, 2023