Questions: Circles and circle theorems
Pick a question type. Each time you get new numbers. Free ones are marked free.
Parts of a circle
- Name the part of a circleChoose, 1 mark, free
- Name the marked partWrite down, 1 mark, free
- Radius, diameter and a squareWork out, 3 marks, free
- Two radii make an isosceles triangleWork out, 2 marks, free
- Radii are equal: form an equationSolve, 4 marks, free
- Perimeter of a triangle made by two radiiWork out, 2 marks, free
The circle theorems
- Angle at the centreWork out, 2 marks, free, Higher tier
- Angle in a semicircleWork out, 2 marks, free, Higher tier
- Angles in the same segmentWork out, 2 marks, free, Higher tier
- Cyclic quadrilateralWork out, 2 marks, free, Higher tier
- Two missing angles in a cyclic quadrilateralWork out, 2 marks, free, Higher tier
- Which theorem is it?Choose, 1 mark, free, Higher tier
- Perpendicular from the centre to a chordWork out, 3 marks, free, Higher tier
- An obtuse angle at the circumferenceWork out, 2 marks, free, Higher tier
- Which statement is true?Choose, 1 mark, free, Higher tier
Tangents
- Tangent and radiusWork out, 2 marks, Plus, Higher tier
- Length of a tangentWork out, 3 marks, Plus, Higher tier
- Two tangents from a pointWork out, 3 marks, Plus, Higher tier
- Two tangents and the chord between themWork out, 4 marks, Plus, Higher tier
- Equal tangents: form an equationSolve, 4 marks, Plus, Higher tier
- The alternate segment theoremWork out, 2 marks, Plus, Higher tier
- Alternate segment, both sidesWork out, 3 marks, Plus, Higher tier
- Give the reasonChoose, 1 mark, Plus, Higher tier
- A circle inside a triangleWork out, 4 marks, Plus, Higher tier
Chains of reasoning
- Centre, then isoscelesWork out, 3 marks, Plus, Higher tier
- Cyclic quadrilateral with a side extendedWork out, 2 marks, Plus, Higher tier
- Semicircle and isosceles togetherWork out, 4 marks, Plus, Higher tier
- Tangent, chord and the centreWork out, 3 marks, Plus, Higher tier
- Two tangents and an angle at the circumferenceWork out, 3 marks, Plus, Higher tier
- Algebra in a cyclic quadrilateralSolve, 4 marks, Plus, Higher tier
- Algebra with the angle at the centreSolve, 4 marks, Plus, Higher tier
- Two chords that crossWork out, 3 marks, Plus, Higher tier
- Name the circle theoremChoose, 1 mark, Plus, Higher tier
- Prove the angle in a semicircle is 90°Prove, 4 marks, Plus, Higher tier
- Centre and cyclic quadrilateral togetherWork out, 2 marks, Plus, Higher tier
The equation of a circle
- Radius from the equationWrite down, 1 mark, Plus, Higher tier
- Equation from the radiusWrite down, 1 mark, Plus, Higher tier
- Inside, on or outside the circleChoose, 2 marks, Plus, Higher tier
- A missing coordinate on the circleWork out, 2 marks, Plus, Higher tier
- Gradient of a tangentWork out, 3 marks, Plus, Higher tier
- Equation of a tangentFind, 4 marks, Plus, Higher tier
- Where a line crosses the circleWork out, 3 marks, Plus, Higher tier
- A circle through a pointWork out, 3 marks, Plus, Higher tier
- Where a tangent meets the x-axisWork out, 4 marks, Plus, Higher tier
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