Maths · OCR Paper 2
Circle Theorems
The circle theorem skills tested on OCR Paper 2: angles at the centre and in a semicircle, same segment and cyclic quadrilaterals, tangents and chords, the alternate segment theorem, and proofs and problems, all done without a calculator.
Lessons
Ticks are remembered on this device only.
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1
Angles at the Centre and in a Semicircle
Using the angle at the centre and the angle in a semicircle, with reasons and radii.
9 terms -
2
Same Segment and Cyclic Quadrilaterals
Using equal angles in the same segment and the opposite angles of a cyclic quadrilateral.
9 terms -
3
Tangents and Chords
Using the tangent and radius, equal tangents, and the perpendicular from the centre to a chord.
9 terms -
4
The Alternate Segment Theorem
Finding angles between a tangent and a chord using the alternate segment theorem.
9 terms -
5
Circle Theorem Proofs and Problems
Proving circle theorems, solving multi-step problems, and finding the equation of a tangent.
9 terms
Key terms in this chapter
All 45, gathered from every lesson.
- Circle theorem
- A rule about angles and lines in a circle.
- Chord
- A straight line joining two points on a circle.
- Arc
- A part of the circumference.
- Tangent
- A line that touches a circle at one point.
- Diameter
- A chord through the centre of a circle.
- Circumference
- The distance around a circle, or the circle itself.
- Subtend
- To make an angle from a chord or arc at a point.
- Semicircle
- Half of a circle, cut by a diameter.
- Reason
- A statement of the theorem that justifies an angle.
- Segment
- The part of a circle cut off by a chord.
- Same segment
- The same side of a chord.
- Cyclic quadrilateral
- A quadrilateral with all four corners on a circle.
- Opposite angles
- Angles in opposite corners of a quadrilateral.
- Exterior angle
- An angle between a side extended and the next side.
- Interior opposite angle
- The inside angle at the opposite corner.
- Supplementary
- Adding up to \(180^\circ\).
- Equation
- A statement that two expressions are equal.
- Reason
- A statement of the theorem that justifies an angle.
- Tangent
- A straight line that touches a circle at one point.
- Chord
- A straight line joining two points on a circle.
- Point of contact
- The point where a tangent touches the circle.
- Perpendicular
- At \(90^\circ\) to a line.
- Bisect
- Cut exactly in half.
- Radius
- The distance from the centre to the circle.
- Kite
- A quadrilateral with two pairs of equal adjacent sides.
- Hypotenuse
- The longest side of a right-angled triangle.
- Isosceles triangle
- A triangle with two equal sides.
- Alternate segment
- The segment on the other side of a chord from a given angle.
- Tangent
- A straight line that touches a circle at one point.
- Chord
- A straight line joining two points on a circle.
- Point of contact
- The point where a tangent touches the circle.
- Segment
- The part of a circle cut off by a chord.
- Isosceles triangle
- A triangle with two equal sides.
- Base angles
- The two equal angles of an isosceles triangle.
- Radius
- The distance from the centre to the circle.
- Reason
- A statement of the theorem that justifies an angle.
- Proof
- A series of steps, with reasons, that shows a result is always true.
- Theorem
- A result that has been proved.
- Exterior angle
- An angle between a side extended and the next side.
- Radius
- The distance from the centre to the circle.
- Isosceles triangle
- A triangle with two equal sides.
- Negative reciprocal
- The number found by turning a fraction upside down and changing its sign.
- Gradient
- A measure of the steepness of a line.
- Tangent
- A straight line that touches a circle at one point.
- Major arc
- The longer arc between two points on a circle.