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ASMaths: PureOCRRevision Notes3. Coordinate Geometry3.2 Circles3.2.5 Radius & Tangent

Radius & Tangent (OCR AS Maths: Pure)

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Radius & Tangent

What is the relationship between tangents and radii?

  • 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 can I find the equation of the tangent line to a circle at a given point?

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 Tip

  • 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

    Author: Roger

    Expertise: Maths

    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.