Tangents to a circle and a line and a circle
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 3 worked examples, 4 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- The line that only touches
- Tangent at a point
Read the transcript of the teaching part
Last time
Before we start: last time, in The equation of a circle and two circles, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
The line that only touches
A bicycle wheel on the road touches it at one point only. That road is a tangent to the wheel. Two facts handle every circle tangent question: the tangent is perpendicular to the radius, and a tangent meets the circle once.
Tangent at a point
A tangent at a point is perpendicular to the radius to that point. Find the gradient of the radius from the centre to the point. Then take the negative reciprocal. Write the line through the point with that gradient. First check the point lies on the circle: substitute it into the equation.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Line meeting a circle · Tangent to a circle.
The whole chapter: Coordinate Geometry.
Chapter 1.3: Coordinate geometry
- Straight lines: mid-points, equations and straight-line form 6 min
- The equation of a circle and two circles 6 min
- Tangents to a circle and a line and a circle 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.