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GCSE Mathematics · key term
The point of contact is the point where a tangent touches a circle.
Used by AQA, Edexcel and OCR
Specification A16 · Paper 1, Paper 2, Paper 3
Revise: Circle EquationsThe radius drawn from the centre to that point of contact is perpendicular to the tangent. Thus the circle tells us the direction of the radius, and perpendicular gradients then tell us the direction of the tangent.
Specification A16 · Paper 1, Paper 2, Paper 3
Revise: Circle EquationsAt that point of contact, the tangent is perpendicular to the radius. This geometrical fact connects circle equations with gradients of straight lines.
After finding the tangent equation, substitute the point of contact back into it. Its coordinates must satisfy the equation.
If the point of contact has , the tangent is horizontal; if it has , the tangent is vertical, so is not suitable.
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Specification 7.02b, 8.05g · Paper 1 (Foundation), Paper 2 (Foundation), Paper 3 (Foundation), Paper 4 (Higher), Paper 5 (Higher), Paper 6 (Higher)
The single point where a tangent meets a circle.
Revise: Parallel and Perpendicular LinesThe radius drawn from the centre to that point of contact is perpendicular to the tangent. This turns a circle problem into a perpendicular-line problem: find the radius's gradient, take its negative reciprocal, and then form the line through the point of contact.
The point where a tangent touches a circle.
In a tangent question, use the gradient of the radius joining the centre to the point of contact—not a different radius.