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Circle Theorems•
Circles•
Lines and Angles

Circle Theorems: Triangles in Circles WORKSHEET

Suitable for Year groups: Year 10, Year 11
GCSE Tier: Higher
Targeting grades: 6-7
Prerequisite knowledge: Calculating missing angles in triangles. Using angle facts such as angles on a straight line and angles around a point.
Learning Objective: Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results.

Circle Theorems: Triangles in Circles WORKSHEET DESCRIPTION

This worksheet focuses on exploring triangles within circles and their associated angle properties.

The first section introduces diagrams involving radii, guiding students to calculate missing angles using their knowledge of angles in isosceles triangles. In the second section, the triangles inscribed in the circles are formed using the diameter. Hence, introducing the theorem “the angle in a semicircle at the circumference”.

With its clear focus on foundational concepts, this worksheet serves as an ideal starting point before teaching more of the standard circle theorems, ensuring students gain confidence in working with triangles in circles.

Three-letter angle notation is used throughout.

All worksheets are created by the team of experienced teachers at Cazoom Maths.

Circle Theorems: Triangles in Circles Worksheet suitable for Year 10 and Year 11 students

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Frequently Asked Questions

Students should be comfortable calculating missing angles in triangles and applying fundamental angle facts such as angles on a straight line and angles around a point. These skills form the foundation for understanding how triangles behave within circles, particularly when working with isosceles triangles formed by radii and applying the angle in a semicircle theorem.