# Can an equilateral triangle fit in a circle?

## Can an equilateral triangle fit in a circle?

Yes. If you’re familiar with construction using compass and straight edge, one of the easiest ways to construct an equilateral triangle is to draw two circles where each circle’s centre lies on the other circle’s edge.

### 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.

What is an equilateral triangle in a circle?

It’s key to know that an equilateral triangle has equal sides and equal angles measuring 60 degrees each. So each angle of an equilateral triangle inscribed in a circle cuts off 1/3 of the circle.

Is a circle an equilateral?

The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest area of all those circumscribed around a given circle is equilateral.

## How many equilateral triangles are in a circle?

A Circle is evenly divided into six equal triangles.

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

It is impossible to create an obtuse equilateral triangle. The word ‘equilateral’ means equal sides.

How do you make an equilateral triangle?

The easiest way is to use a protractor to draw three 120° angles around the center of the circle, and then connect the three points on the circle where the three angles intersect the circumference. That will result in an inscribed equilateral triangle.

What is the radius of a circle inscribed in a triangle?

Hence the radius of the inscribed circle is 3. Here a and b are the sides and c is the hypotenuse of the right angled triangle. This is used when the circle is inscribed in a right angled triangle.

## Which circle is inscribed in a triangle?

incircle
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle’s incenter.

a straight line extending from the center of a circle or sphere to the circumference or surface: The radius of a circle is half the diameter. a circular area having an extent determined by the length of the radius from a given or specified central point: every house within a radius of 50 miles.

How many equilateral triangles are there in a circle?

How do you draw a scalene triangle?

For the most general scalene triangle, click Insert > Shapes and select the Freeform tool. Click (but don’t drag) the mouse cursor at the first, second, and third corners and then double-click at the first corner to close the shape. It’s also possible to draw a scalene triangle with one…

## How do you find the sides of an equilateral triangle?

If you’re trying to find a side other than the hypotenuse, square the side given, subtract it from the hypotenuse squared, and take the square root of the answer. Recognize that an equilateral triangle has three equal sides.

### What is an equatorial triangle?

In geometry, an equilateral triangle is a triangle where all three sides are the same length and all three angles are also the same and are each 60 ° . If an altitude is drawn, it bisects the side to which it is drawn, in turn leaving two separate 30-60-90 triangles.