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: 4 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
- 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.
Chapter 8: Coordinate geometry of the circle
- The equation of a circle and two circles 5 min
- Tangents to a circle and a line and a circle 6 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.