How do you find the circumradius of a polygon?

The circumradius of a polygon is the radius of its circumcircle. The formula for the circumradius of a triangle with sides of lengths a, b, and c is (abc) / sqrt((a + b + c)(b + c – a)(c + a – b)(a + b – c)), and for a regular polygon with n sides of length s, it is s / (2sin(π / n)).

How do you find the area of a triangle with circumradius?

Formula 3: Area of a triangle if its circumradius, R is known. Area, A = abc4R, where R is the circumradius.

What is the circumradius of a polygon?

The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed. Similarly, the circumradius of a polyhedron is the radius of a circumsphere touching each of the polyhedron’s vertices, if such a sphere exists.

What is circumradius and inradius of a triangle?

Inradius The inradius( r ) of a regular triangle( ABC ) is the radius of the incircle (having center as l), which is the largest circle that will fit inside the triangle. Circumradius: The circumradius( R ) of a triangle is the radius of the circumscribed circle (having center as O) of that triangle.

What is the circumradius of a cyclic polygon?

The circumradius of a cyclic polygon is the radius of the circumscribed circle of that polygon. For a triangle, it is the measure of the radius of the circle that circumscribes the triangle. Since every triangle is cyclic, every triangle has a circumscribed circle, or a circumcircle .

How to find the circumradius of a triangle?

If a triangle has side lengths a, b, and c, then we can find the length of its circumradius using the following formula: This may look like a complicated formula, but when we plug in values for a, b, and c, we’ll find that it really isn’t too bad. For example, suppose we have a triangle with side lengths 6 inches, 8 inches, and 10 inches.

How to find the area of a triangle?

Area of a triangle given its circumradius and inradius. A triangle has inradius 4 cm and a circumradius of 65 8 cm. Find its area. I let the sides of the triangle be a, b, and c.

How to calculate the relation between inradius and circumradius?

Formula of Inradius is, r = (a + b – c) / 2 relation between circumradius and inradius of equilateral triangle Relation between circumradius and inradius of an equilateral triangle is in such a way that Inradius of a circle is equal to the half of the Circumradius of a circle.