## Equilateral triangle inscribed in a circle

This page demonstrates how to use a compass and a straightedge or ruler to draw an equilateral triangle inscribed in a circle, which is similar to drawing an inscribed hexagon except we use every other vertice instead of all six for each side of the circle.

### Explanation of method

Instead of drawing a hexagon, we make a triangle with every other point; both are regular polygons, but one has twice as many sides as the other and three equal arcs.

### Proof

Steps 1 through 7 are the same as for making a hexagon inscribed in a circle, except we use every other point on the circle to figure out which one is congruent with the others in the case of an inscribed equilateral triangle.

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

If you don’t have a compass, you can draw the triangle without using the circle guide by carefully measuring each side with a ruler; because each angle is related to the length of the sides as described by the Law of Cosines, all the angles will be equal when all the sides are equal.

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

This is the largest equilateral triangle that will fit in the circle, with each vertex touching the circle; it’s similar to making an inscribed hexagon, except we use every other vertex instead of all six.

## How do you construct a triangle in a circle?

Make a circle out of a triangle.

- Bisect one of the angles.
- Bisect another angle.
- The incenter is the center of the inscribed circle.
- Build a perpendicular from the center point to one of the triangle’s sides.

## How do you make a perfect equilateral triangle?

The simplest method is to draw three 120u00b0 angles around the circle’s center with a protractor, then connect the three points on the circle where the three angles intersect the circumference, resulting in an inscribed equilateral triangle.

## What is the shortest side of a 30 60 90 triangle?

Explanation: In a 30-60-90 right triangle, the shortest side is half of the hypotenuse, which is opposite the 30 degree angle.

## What is the radius of equilateral triangle?

The radius of an equilateral triangle’s circumcircle is equal to (a / 3), where ‘a’ is the length of the triangle’s side.

## What is the radius of Incircle of equilateral triangle?

, where r is the radius of the given circle, and the radius of an equilateral triangle’s Incircle = (equilateral triangle’s side)/ 3.

## What is the Orthocentre of a triangle?

The orthocenter of a triangle is the point where the triangle’s three altitudes intersect. Altitude – A triangle’s altitude is the line that passes through its vertex and is perpendicular to the opposite side; thus, a triangle can have three altitudes, one from each vertex.

## What is Circumcircle in a triangle?

The circumcircle is the circumscribed circle of a triangle, that is, the unique circle that passes through each of the triangle’s three vertices; the circumcenter is the circumradius, and the circumradius is the circumradius.

## How do you construct a circle?

The Circle’s Construction

- Place the metal tip on the center point.
- Spread the compass according to convenience or given radius.
- Measure the distance between the tips of the compass and the pencil using the ruler to align with the desired radius.

## Is it possible to draw an obtuse equilateral triangle?

It is impossible to make an obtuse equilateral triangle because the term “equilateral” refers to a triangle with equal sides.