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.
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.