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

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

The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa2/12. Lets see how this formula is derived, Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle.

What is the relation between a circle and an equilateral triangle which is inscribed in the circle?

The relation between the side of the equilateral triangle and the radius of circumcircle is, a = √3×r. P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle.

What is the inscribed circle of an equilateral triangle?

The Incircle of a triangle Also known as “inscribed circle”, it is the largest circle that will fit inside the triangle. Each of the triangle’s three sides is a tangent to the circle. Try this Drag the orange dots on each vertex to reshape the triangle.

What is the radius of a circle inscribed in an equilateral triangle?

For finding the radius of the circle use the formula r=(s−a)tanA2 and the known thing that s of a equilateral triangle is half of three times of its sides and all angles are equal to 60∘.

What is the radius of circle inscribed in an equilateral triangle?

What is the radius of a circle inscribed in an equilateral triangle ABC of side 4 cm?

Join OA, OB and OC. Let the radius of the circle be r cm. Therefore, the radius of the inscribed circle is 3.46 cm.

Can a circle be inscribed in a triangle?

A circle can be inscribed in any triangle, whether it is isosceles, scalene, an equilateral triangle, an acute-angled triangle, an obtuse angled triangle or a right triangle. And incentre of a triangle always lies inside the triangle. To construct an incircle, we require a Ruler and a Compass.

What is the incircle of a triangle called?

Define Incircle of a Triangle A circle drawn inside a triangle such that it touches all the three sides of the triangle is called the incircle of a triangle. The sides of the triangle which touches the circle are tangents to the circle. Hence, the centre of the circle is situated at the intersection of the triangle’s internal angle bisectors.

What is the radius of the incircle of an equilateral triangle?

Let the side of an equilateral triangle = a. Then, the area of an equilateral triangle = 3 4 × a 2. Therefore, the radius of the incircle of an equilateral triangle is given by r = 2 × A r e a o f a n e q u i l a t e r a l t r i a n g l e P e r i m e t e r o f a n e q u i l a t e r a l t r i a n g l e

What is the centre of a circle called?

Hence, the centre of the circle is situated at the intersection of the triangle’s internal angle bisectors. This point is known as the incentre of the triangle and it is always equidistant from the sides of the triangle. The length of the perpendicular is called the inradius.