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?
- Find the gradient of the radius OP
- Find the gradient of the tangent
- 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)
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.