## Can an equilateral triangle be inscribed in a circle?

180 ∘ ÷ 3 = 60 ∘ . Circle: A planar figure that consists of points that are the same distance (the radius) from a fixed point (the center). Equilateral triangle inscribed in a circle: This occurs when the vertices of the equilateral triangle are on the circle.

## How do you draw an equilateral triangle in a circle without a compass?

However, if you do not have a compass, you can draw the triangle without using the circle guide by measuring each side carefully with a ruler. Because each angle is related to the length of the sides as described by the Law of Cosines, when all the sides are equal, all the angles will also be equal.

How do you construct an equilateral triangle inscribed in a circle in geogebra?

1) Using the POINT TOOL & SEGMENT TOOL, label point C on circle A to create diameter CB. 2) Using the COMPASS TOOL, create a circle with radius AB and center point B 3) Using the POINT TOOL, mark points D and F where circle A intersects circle B. 4) Using the SEGMENT TOOL, draw a segment from point D to point F.

What do you call a triangle inside a circle?

Circumscribed circles When a circle circumscribes a triangle, the triangle is inside the circle and the triangle touches the circle with each vertex. You use the perpendicular bisectors of each side of the triangle to find the the center of the circle that will circumscribe the triangle.

### How many equilateral triangles are there in a circle?

A Circle is evenly divided into six equal triangles.

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

Length BD=length DC. 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.

How do you draw a equilateral triangle in a circle without a compass?

How do you make an incenter?

To construct the incenter, first construct the three angle bisectors; the point where they all intersect is the incenter. The incenter is always located within the triangle. One of the four special types of points of concurrency inside a triangle is the incenter.

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

1. In an equilateral triangle the center of the circle in which it is inscribed divides the altitude in the ratio 2:1 which is a property.
2. hence 2x+1x=altitude.
3. altitude =3x.
4. of which the 2x portion is the radius hence 2x=3.
5. which implies x=1.5units.
6. so altitude is 3*x=3*1.5=4.5units.
7. hence the answer is 4.5 Units.