Radius & Tangent (OCR AS Maths: Pure)

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)