Reach for the Star | GCSE Mathematics

L081: Circle geometry pathway

Objective

Use circle geometry at the appropriate tier and explain angle reasoning.

Calculator: Non-calculator core; calculator optional only for checking where labelled.

Visual model for Circle geometry pathway
Points route: Connect 2 · Share 2 · Apply 6 · Review 3 · Stretch 2 · Deep Challenge 3. Record your score honestly after you have checked your answer.

Recall

Retrieve the key fact or method needed for circle geometry pathway.

Core practice

A central angle is 146°. Find the circumference angle subtending the same arc.

Reasoning

In a cyclic quadrilateral, opposite angles are 2x+10 and 3x−5. Find x and both angles.

Exam-style

Use a labelled diagram to calculate the missing value. State the theorem or formula and include units where needed.

WWW / EBI

Recall & Review: feedback and extension integration

Lesson L081: Circle geometry pathway

Objective: Use circle geometry at the appropriate tier and explain angle reasoning.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.

Even Better If (EBI)

I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.

Stretch and deep challenge

Stretch: A central angle is 146°. Find the circumference angle subtending the same arc.

Deep challenge: In a cyclic quadrilateral, opposite angles are 2x+10 and 3x−5. Find x and both angles.