Two radii form an isosceles triangle

Martin McBride, 2020-08-16
Tags circle isosceles triangle radius
Categories maths gcse geometry

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

Since it is a 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.

This theorem is covered in this video on circle theorems:

Proof

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

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GCSE geometry

1. GCSE geometry
2. Geometry rules
3. Parallel lines
4. Polygons
5. - Regular polygons
6. - Triangles
7. - Quadrilaterals
8. - More quadrilaterals
9. - Interior/exterior angles
10. Circle geometry
11. - Tangent and radius
12. - Two radii
13. - Chord bisector
14. - Angle at centre
15. - Angle in semicircle
16. Transformations
17. Loci
18. - Fixed distance from a point
19. - Fixed distance from a line
20. - Equal distance between 2 lines
21. - Equal distance between 2 points

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