Tangents to Circles
What is a tangent to a circle?
- A tangent is a line that touches a circle at a single point but doesn't cut across the circle
How is a tangent to a circle related to the radius?
- 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: We'll now know a point on the (tangent) line (x2, y2) and it's gradient, m, say
- Substituting these into allows us to find c
- i.e.
- Then we can write down the equation of the tangent in the form
- You could alternatively use the form for the equation of the line
- Substituting these into allows us to find c
Exam Tip
- 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