Table of Contents
- 1 How do you find the area of an inscribed circle in a equilateral triangle?
- 2 What is the area of an equilateral triangle whose inscribed circle has radius?
- 3 How is the area of a circle inscribed in an equilateral triangle related to the area of a circle circumscribed around that same triangle?
- 4 What is the radius of circle inscribed in a equilateral triangle?
- 5 How do you solve an inscribed circle?
- 6 How do you find the radius of an equilateral triangle in a circle?
How do you find the area of an inscribed circle in a 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 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 inscribed circle?
When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units. The area of a circle of radius r units is A=πr2 .
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.
How is the area of a circle inscribed in an equilateral triangle related to the area of a circle circumscribed around that same triangle? The area of the inscribed circle is 1/2 the area of the circumscribed circle.
What is the radius of circle inscribed in a 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 height of equilateral triangle inscribed in a circle?
Using the properties of 30˚−60˚−90˚ triangles, it can be determined that h=1 and s2=√3 . Thus, s=2√3 and the height of the triangle can be found through a+h=2+1=3 .
What is the radius of Incircle of equilateral triangle?
Also the radius of Incircle of an equilateral triangle = (side of the equilateral triangle)/ 3.
How do you solve an inscribed circle?
By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc. The measure of the central angle ∠POR of the intercepted arc ⌢PR is 90°. Therefore, m∠PQR=12m∠POR =12(90°) =45°.