Questions that need two or three facts in a row, with algebra, and a short proof.
What you will learn
- Combine circle theorems with isosceles triangles and straight lines
- Form and solve equations from circle theorems
- Prove a circle theorem from isosceles triangles
One step, one reason
Most marks are lost by jumping.
Write each angle on its own line with its reason, then use it.
- angle AOB = 2 × 35 = 70° (the angle at the centre is twice the angle at the circumference)
- OA = OB (radii), so triangle OAB is isosceles
- angle OAB = (180 − 70) ÷ 2 = 55° (base angles of an isosceles triangle are equal)
The rest of this lesson and its 8 practice questions are locked.
In this lesson
- One step, one reason
- Where to start
- Proving a theorem
- Algebra
- Try it: First question
8 practice questions, marked as you go; about 25 minutes in all.
Key terms
Centre and cyclic quadrilateral, Crossing chords
In this unit: Circles and circle theorems
The parts of a circle, the circle theorems and how to give them as reasons, tangents, chains of reasoning, and the equation of a circle centred at the origin with its tangents.
- Parts of a circle
- The circle theorems
- Tangents
- Chains of reasoning
- The equation of a circle