Circles and chords, sectors in r and theta, and tangents with sectors
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Algebra meets arcs
- From the equation to the circle
- The angle at the centre
Read the transcript of the teaching part
Last time
Before we start: last time, in Arc length, sector area and shaded regions, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Algebra meets arcs
The Paper 1 favourite: a circle on coordinate axes, a chord, and an area in radians. Coordinates give the centre, the radius and the chord. Radians turn those lengths into an angle. Then arc length and sector area do the rest. The marks come from keeping the two halves joined together.
From the equation to the circle
The circle x squared plus y squared minus 14x plus 8y plus 36 equals zero. Halve the coefficients: the centre is 7, minus 4. The radius squared is 7 squared plus 4 squared minus 36, which is 29. So r is root 29. Put y equals minus 2 in: x squared minus 14x plus 24 equals zero. So x is 2 or 12.
The angle at the centre
Drop a line from C to the middle of AB. Half the chord is 5. The distance from C to the chord is 2. So tan of half the angle is 5 over 2. The angle ACB is 2 times inverse tangent of 2.5, which is 2.38 radians. Use radians for area. Keep the unrounded value in your calculator, and round only at the end.
Chapter 1.4: Circular measure
- Arc length, sector area and shaded regions 6 min
- Circles and chords, sectors in r and theta, and tangents with sectors 6 min
Also for A Level Maths 9709 Paper 1
Which topics come up most in A Level Maths 9709 Paper 1 past papers, counted from every paper since 2004.