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Tangents to Circles (CIE IGCSE Additional Maths)
Revision Note
Tangents to Circles
What is a tangent to a circle?
- A tangent (to a circle) is a line that touches the circle at a single point but does not 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
As they are perpendicular, if the gradient of the radius is , then, the gradient of the tangent is
(Negative reciprocal)
Alternatively,
- STEP 3
The equation of the tangent is the equation of the line with that gradient that goes through point P (x2, y2)
Write down the equation using where is the gradient
Examiner Tip
- If you understand the formula in Step 2 above
Gradient of tangent
you can find the gradient of the tangent directly without having to find the gradient of the radius first.
Worked example
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