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Radius & Tangent (Cambridge (CIE) AS Maths): Revision Note

Exam code: 9709

Roger B

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Roger B

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Cambridge (CIE) Maths: Pure 1AQA Maths: PureOCR Maths A: PureEdexcel Maths: Pure

Radius & tangent

What is the relationship between a tangent and a radius?

  • A tangent is a line that touches a circle at a single point but doesn't cut across the circle

 

Tangent, A Level & AS Level Pure Maths Revision Notes

  • A tangent to a circle is perpendicular to the radius of the circle at the point of intersection

Tangent Radius, A Level & AS Level Pure Maths Revision Notes

 

How do I find the equation of a tangent to a circle?

Tangent Radius Illustr_1, A Level & AS Level Pure Maths Revision Notes

  •  STEP 1: Find the gradient of the radius OP

 

Tangent Radius Illustr_2, A Level & AS Level Pure Maths Revision Notes

  • STEP 2: Find the gradient of the tangent

Tangent Radius Illustr_3, A Level & AS Level Pure Maths Revision Notes

  • STEP 3: The equation of the tangent is the equation of the line with that gradient that goes through point P (see Equation of a Straight Line)

Examiner Tips and Tricks

  • If you understand the formula in Step 2 above, you can find the gradient of the tangent without having to find the gradient of the radius first.

Worked Example

Radius & Tangent Example, A Level & AS Level Pure Maths Revision Notes
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Roger B

Author: Roger B

Expertise: Maths Content Creator

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.