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

 May 23, 2023
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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

 May 23, 2023

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