Triangle in a Circle Calculator Online

The Triangle in a Circle Calculator is a valuable tool designed to facilitate the solution of geometric problems involving triangles inscribed within circles. It assists in determining fundamental properties of such triangles, including their area, perimeter, and the radius of the circumscribing circle. Tailored for students, educators, and professionals in fields such as mathematics, engineering, and architecture, this calculator provides swift and accurate calculations to streamline geometric analyses.

Formulas of Triangle in a Circle Calculator

Given the Radius of the Circle (r):

Area of the Triangle (A): A = (1/2) * r * P

Perimeter of the Triangle (P): P = 2 * r * π

Given the Side Lengths of the Triangle (a, b, c):

Area of the Triangle (A): A = sqrt(s * (s – a) * (s – b) * (s – c))

Where: s = (a + b + c) / 2

Radius of the Circle (r): r = (a * b * c) / (4 * A)

General Terms Table

Term	Definition
Inscribed Triangle	A triangle whose vertices lie on the circumference of a circle.
Circumscribed Circle	A circle that passes through all the vertices of a triangle.
Perimeter	The total length of the boundary of a geometric figure.
Area	The measure of the space enclosed by a geometric figure.
Radius	The distance from the center of a circle to any point on its circumference.

Example of Triangle in a Circle Calculator

Suppose we have a circle with a radius of r = 5 units. We want to find the properties of a triangle inscribed within this circle, with side lengths of a = 4 , b = 7 , and c = 8 units.

1. **Area of the Triangle A :

A = \sqrt{(s \cdot (s - a) \cdot (s - b) \cdot (s - c))}

s = \frac{a + b + c}{2} = \frac{4 + 7 + 8}{2} = 9.5

A = \sqrt{(9.5 \cdot (9.5 - 4) \cdot (9.5 - 7) \cdot (9.5 - 8))}

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