Radius & Tangent (Edexcel AS Maths) : Revision Note
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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

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

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

STEP 1: Find the gradient of the radius OP

STEP 2: Find the gradient of the tangent

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

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