The angle at the centre, angles in a semicircle and in the same segment, cyclic quadrilaterals, tangents, the alternate segment theorem and chords, with reasons.
7 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
“Giving reasons” is the whole game in circle geometry. Learn eight short statements — and the diagram that goes with each — and every circle question becomes a chain of reasons.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Move the points on the circle.
Copy these into your notebook in your own words — that is how they stick.
Angle at the centre = 2 × angle at the circumference (same arc).
Angle in a semicircle = 90°.
Angles in the same segment (same chord, same side) are equal.
Opposite angles add to 180°; exterior angle = interior opposite angle.
Tangent ⟂ radius; tangents from an external point are equal in length.
Tangent–chord angle = angle in the alternate segment.
Perpendicular from the centre bisects the chord.
Always state the theorem next to each angle — the reason is worth a mark.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (18 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [9 marks]
A, B, C and D are points on a circle with centre O. Angle AOC = 124°, where B and D lie on opposite arcs. The tangent at A makes an angle with the chord AC.
(a) Find angle ABC (B on the major arc). State the reason. [2]
(b) Find angle ADC (D on the minor arc). State the reason. [3]
(c) State the angle between the tangent at A and the chord AC, with the reason. [2]
(d) Triangle OAC has OA = OC. Find angle OAC, with a reason. [2]
Question 2 [9 marks]
PT is a tangent to a circle with centre O and radius 5 cm at T. OP = 13 cm.
(a) State the size of angle OTP with a reason. [2]
(b) Calculate PT. [3]
(c) The second tangent from P touches the circle at S. State the length of PS and the reason. [2]
(d) A chord of the same circle (radius 5 cm) is 8 cm long. Find its distance from the centre. [2]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.