What is the radius of Incircle of equilateral triangle?
Height of equilateral triangle = 18 cm. ∴ The radius of incircle of the given equilateral triangle is 6 cm.
How do you find the area of a circle inside 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 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 do you find the radius of the incircle of a triangle?
Calculating the radius Its radius, the inradius (usually denoted by r) is given by r = K/s, where K is the area of the triangle and s is the semiperimeter (a+b+c)/2 (a, b and c being the sides).
What is the ratio of radius of the incircle of an equilateral triangle to the radius of the Circumcircle of a regular hexagon having sides in the ratio 1 1?
∴ The ratio is 1 : 4.
How is the area of a circle inscribed in an equilateral triangle related to the area of a circle circumscribed around that same 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 the circle inscribed in an equilateral triangle ABC of sides 4 cms?
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.
How do you find the side length of an equilateral triangle inscribed in a circle?
- If we consider triangle ABC , is that equilateral triangle inscribed in the given circle with radius r = 3.2 cm.
- Then, median of the triangle = r + r/2.
- = 3.2 + 1.6 = 4.8 cm.
- If side of the triangle = a cm.
- Then by Pythagoras law, a² = 4.8² + (a²/4)
- => 4a² = 4.8² *4 + a²
- => 3a² = 4.8² * 2²
- => a² = ( 4.8² * 2² ) / 3.
What is the circumcircle of a triangle?
The circumcircle always passes through all three vertices of a triangle. Its center is at the point where all the perpendicular bisectors of the triangle’s sides meet. This center is called the circumcenter. See circumcenter of a triangle for more about this.
What is circumscribed circle?
Circumcircle of a triangle A circle which passes through all three verticesof a triangle Also “Circumscribed circle”. Try thisDrag the orange dots on each vertexto reshape the triangle. Note that the circumcircle always passes through all three points.
What is the radius of a circle in an equilateral triangle?
In an equilateral triangle the center of the circumscribing circle will be at a distance of 2/3 * the altitude of the triangle from any vertex to the opposite side. This distance of 2/3 altitude is the radius of the circle. The diameter of the circle will be 4/3 times the altitude.
How do you find the diameter of a circum circle?
The diameter of the circumcircle is given by the formula: where a is the length of one side, and A is the angle opposite that side. This gives the diameter, so the radus is half of that. This is derived from the Law of Sines.