The right angle between a tangent and a radius, two equal tangents from a point, and the alternate segment theorem.
What you will learn
- Use the 90° between a tangent and the radius
- Use equal tangents from a point
- Use the alternate segment theorem
- Find tangent lengths with Pythagoras
Tangent and radius
A tangent touches the circle at one point, T.
The radius OT meets it at exactly 90°. So triangle OTP, for any point P on the tangent, is right-angled at T: use angle facts or Pythagoras, with OP as the hypotenuse.
Not drawn accurately
- OP² = 5² + 12² = 25 + 144 = 169
- OP = 13 cm
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Tangent and radius
- Two tangents from one point
- The alternate segment theorem
- Try it: Tangent and chord
7 practice questions, marked as you go; about 25 minutes in all.
In this unit: Circles and circle theorems
The parts of a circle, the circle theorems and how to give them as reasons, tangents, chains of reasoning, and the equation of a circle centred at the origin with its tangents.