Circle Theorem: Two Radii Make an Isosceles Triangle
(KS3, Year 8)

homegeometrytwo radii make an isosceles triangle
Two radii of a circle form the two equal sides of an isosceles triangle. circle_theorem_two_radii_make_isosceles_triangle Note: Radii is the plural of radius.

Why Do Two Radii Make an Isosceles Triangle?

A radius is the line segment from the center of the circle to any point on the circle. The length of this line is also called the radius.

circle radius explained A circle is a set of points that are all the same distance from the center. The radius is the same wherever in the circle it is drawn.

radius same lengths Two radii will be of equal length.two_radii_same_lengthsA triangle can be drawn by joining the ends of the two radii together.two_radii_triangleTwo sides of this triangle are the radii of the circle and the same lengths. A triangle with two equal sides is an isosceles triangle.

Lesson Slides

The slider below shows a real example which uses the circle theorem that two radii make an isosceles triangle.

What Is a Circle?

A circle is a shape containing a set of points that are all the same distance from a given point, its center.

What Is an Isosceles Triangle?

An isosceles triangle is a triangle with two equal sides and two equal angles across from them.

isosceles triangle

Interior Angles of an Isosceles Triangle

Two of the interior angles of an isosceles triangle are equal. There are two different angles in an isosceles triangle: the base angle and the vertex angle.

angles in isosceles mini The interior angles of any triangle always add up to 180°. The two base angles are equal. This means that:

Vertex angle = 180° − 2 × Base angle

Base angle = (180° − Vertex angle) ÷ 2

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This page was written by Stephen Clarke.

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