Two radii form an isosceles triangle

By Martin McBride, 2023-01-22
Tags: circle isosceles triangle radius
Categories: gcse geometry


A triangle formed by two radii of a circle is always an isosceles triangle.

Here is a video on the topic:

Isosceles triangles

An isosceles triangle is a triangle that has two equal sides, like this:

Isosceles triangle

The two angles at the base of an isosceles triangle are always equal.

Two radii of a circle

Two radii form the two equal sides of a triangle. The third side is formed by the chord that joins the ends of the two radii.

Two radii form an isosceles triangle

Since it is an isosceles triangle, it follows that the angles between the two radii and the chord that forms the third side of the triangle are also equal.

Proof

A circle is a set of points that are all the same distance from the centre.

A radius is a line drawn from the centre to any point on the circle.

Two radii form an isosceles triangle

Since every point on the circle is the same distance from the centre, every radius is the same length no matter where it is drawn.

Two sides of the triangle are radii of the circle and therefore have the same length. Any triangle with two equal sides is an isosceles triangle, by definition.

Since it is an isosceles triangle, the two angles A and B are also equal. This fact is sometimes useful, for example:

Two radii form an isosceles triangle

It might not be immediately obvious what the angle x is. But if we remember that the triangle is an isosceles triangle we can see very easily that x is equal to the other angle at the base, so it is 70 degrees.

See also



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