Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Circle theorems: tangents and radii
Geometry
CCSS HSG.C.A.2CCSS HSG.C.A.4England: GCSE Higher Geometry
Objective and success criteria
Students will: Circle theorems: tangents and radii.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Circle theorems; Pythagoras' theorem
Leads to: Circle theorems: the alternate segment theorem
Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Circle theorems; Pythagoras' theorem). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A tangent meets a radius at the point of contact. A triangle formed with the centre has an angle of 39° at the centre. What is the angle between the tangent and the line to the centre (the third angle)? → 51Prompt: A tangent is perpendicular to the radius at the point of contact.
- Two angles at the circumference stand on the same arc. One is 65°. What is the other? → 65Prompt: Angles in the same segment are equal.
- ABCD is a cyclic quadrilateral. Angle A = 102°. What is angle C? → 78Prompt: Opposite angles in a cyclic quadrilateral add up to 180°.
Hook · 3 min
- Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
- Share the objective: Circle theorems: tangents and radii. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 49°. Find ∠AOB.
- Step 1: ∠OAP = ∠OBP = 90°
- Step 2: ∠AOB = 360° − 90° − 90° − 49° = 131°
- Answer: 131
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 30°. Find ∠AOB. → 150Prompt: A tangent meets the radius at 90°.
- Two tangents are drawn from point P to a circle, touching it at A and B. PA = (1x + 12) cm and PB = (2x + 7) cm. Find x. → 5Prompt: Tangents from the same point are equal in length.
You do: independent practice · 7 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Two tangents are drawn from point P to a circle, touching it at A and B. PA = (1x + 22) cm and PB = (3x + 10) cm. Find x. → 6Prompt: Tangents from the same point are equal in length.
- PA and PB are tangents from P to a circle with centre O, touching it at A and B. ∠APB = 103°. Find ∠AOB. → 77Prompt: A tangent meets the radius at 90°.
Watch out for
- Thinking a square turned on its corner is no longer a square.
- Reading the wrong scale on a protractor.
Support and stretch
Support
- Review first: Circle theorems.
- Use concrete materials: rulers and protractors.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Circle theorems: the alternate segment theorem.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-10.
Free lesson plan from eurekami.com/lesson-plan-builder