Radius & Tangent (Cambridge International AS Mathematics)

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

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

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

• 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)

Exam Hint

• 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