Geometry & MeasuresStudy Notes

Worked Example 2

Part of Properties of CirclesGCSE Mathematics

This study notes covers Worked Example 2 within Properties of Circles for GCSE Mathematics. Revise Properties of Circles in Geometry & Measures for GCSE Mathematics with 10 exam-style questions and 4 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 4 of 5 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 5

Practice

10 questions

Recall

4 flashcards

Worked Example 2

A tangent touches a circle at point P. The radius OP meets the tangent at P. What is the angle between the radius and the tangent?

Solution

Key circle theorem: A tangent meets a radius at 90 degrees

The tangent touches the circle at point P

OP is the radius to point P

Therefore, the angle between them is 90 degrees

This is always true for any tangent and radius at the point of contact

Keep building this topic

Read this section alongside the surrounding pages in Properties of Circles. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Properties of Circles

A triangle is drawn inside a circle with one side being the diameter. What is the size of the angle at the circumference opposite the diameter?

  • A. 45°
  • B. 60°
  • C. 90°
  • D. 180°
1 markfoundation

Prove that the angle in a semicircle is 90°, using the theorem that the angle at the centre is twice the angle at the circumference.

3 markshigher

Quick Recall Flashcards

Tangent Rule
A tangent ALWAYS meets the radius at 90° at the point of contact.
Tangent
Line touching circle at one point, perpendicular to radius

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