What is the area of an equilateral triangle whose inscribed circle has radius?

So, the area of the inscribed equilateral triangle is equal to three times the area of the equilateral triangle whose each side is equal to the radius of the circle.

How do you find the area of an equilateral triangle circumscribed in a circle?

We know that area of circle = π*r2, where r is the radius of given circle. We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ √3. Therefore, area = π*r2 = π*a2/3.

What is an inscribed triangle?

An inscribed triangle is a triangle inside a circle. To draw an inscribed triangle, you first draw your triangle. Then you draw perpendicular bisectors for each side of the triangle. Where they meet is the center of your circle.

When a triangle is inscribed in a circle?

When a circle inscribes a triangle, the triangle is outside of the circle and the circle touches the sides of the triangle at one point on each side. The sides of the triangle are tangent to the circle. draw in the angle bisectors. The intersection of the angle bisectors is the center of the inscribed circle.

When equilateral triangle is inscribed in a circle?

Let ABC be an equilateral triangle inscribed in a circle of radius 6 cm. Let O be the centre of the circle. Then, OA = OB = OC = 6 cm. Let OD be perpendicular from O on side BC.

What is the area of the largest triangle that is inscribed in a semicircle of radius R unit?

The area of the largest triangle that can be inscribed in a semi-circle of radius ‘r’ is: r2. 2r2.

How do you find the radius of an equilateral triangle?

The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa 2/12. Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle.

What is an equilateral triangle in geometry?

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; all three internal angles are also congruent to each other and are each 60°.

How do you find the area of a circle inside a triangle?

The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa 2/12. Lets see how this formula is derived, Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle. Area of triangle of side a = (√3)a 2/4.

How to find the radius of the inscribed circle inside triangle?

The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa 2 /12. Lets see how this formula is derived, Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle.