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

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

The circle is inscribed in the triangle, so the two radii, OE and OD, are perpendicular to the sides of the triangle (AB and BC), and are equal to each other.

### When a circle is 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 length of an equilateral triangle inscribed in a circle?

Total length BC= BD+DC. BC=2×3√3=6√3cm. Note: If the question was given for isosceles triangle instead of equilateral triangle, the OA≠OB≠OC ≠radius.

When constructing an equilateral triangle by hand which step comes after constructing a circle?

When constructing an equilateral triangle by hand, which step comes after constructing a circle? Set compass to the radius of the circle. You just studied 10 terms!

When a 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 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.

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

Also, we know that s of an equilateral triangle is half of three times of its sides and all angles are equal to 60∘. We know that tan30∘=1√3 . Now the diameter of the circle is twice its radius, so the length of the diameter is 2r=a√3 .

#### 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.

What is the second step in constructing equilateral triangle?

Steps

1. Start by drawing the base of the triangle as a line with two end points.
2. Using a compass place the spike of the compass at one point and the drawing tip at the second point and draw an arc upwards.
3. Repeat the step above for the other point.
4. Draw a dot at the point where the two arcs intersect.