Year 10 Circle Theorems Worksheets (GCSE) | Printable PDFs
Year 10 Circle Theorems Worksheets for students in year 10, aged 14-15. Circle theorems are rules that describe the relationships between angles, chords, tangents, and radii in a circle. These theorems allow students to calculate missing angles and lengths without measuring.
Some of the most common circle theorems include angles in the same segment being equal, the angle at the centre being twice the angle at the circumference, and angles in a semicircle being 90°. Students also learn that a tangent is perpendicular to the radius at the point of contact and that opposite angles in a cyclic quadrilateral add up to 180°.
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Circle Theorems
Common Questions about Year 10 Circle Theorems
What is a circle theorem?
A circle theorem is a rule about angles, chords, radii and tangents in a circle that can be used to solve geometric problems.What angle is formed between a tangent and a radius?
A tangent is always perpendicular to the radius at the point of contact, so the angle formed is 90°.Which circle theorem is used most often?
A common theorem states that the angle at the centre of a circle is twice the angle at the circumference on the same arc.
Year 10 Circle Theorems Common Mistakes
Common Mistake 1
A common mistake is using the wrong circle theorem because the centre, circumference, chord or tangent has not been identified correctly.Common Mistake 2
Students often forget that a tangent is perpendicular to the radius at the point of contact, so they miss the 90° angle.Common Mistake 3
Another common mistake is giving an angle answer without a reason, even though circle theorem questions often require clear geometric reasoning.
Circle Theorems Worksheets - Free Worksheets Above
Angles in Circles (A)
Angles in Circles (B)
Tangents to Circles