What is a tangent?

• A tangent to a circle is a straight line outside of the circle that touches its circumference only once
• Tangents are the easiest thing to spot quickly in a circle theorem question as they lie outside of the circle and stand out clearly

Circle Theorem: A radius and a tangent are perpendicular

• Most of the time, if there is a tangent in a circle theorem question it will meet a radius at the point where it touches the circumference of a circle
  • Make sure that the line the tangent meets is definitely a radius; that it starts at O, the centre
• This circle theorem states that a radius and a tangent meet at 90°
  • Perpendicular just means at right angles
• If asked to state reasons and you use this theorem then use the key phrase;
  • "A radius and a tangent meet at right angles"

What else should I know about tangents?

• Although it is not strictly a circle theorem the following is a very important fact for solving some problems
• Two tangents from a circle to the same point outside of a circle are equal length
• This means that a kite can be formed by two tangents meeting a circle
  • Remember that a kite is essentially two congruent triangles about its main diagonal
  • The kite will have two right angles, where the tangents meets the radii