Angle rules in circles

What this chapter teaches

In a circle the angle at the centre is double the angle at the circumference on the same arc. So the angle in a semicircle is 90°, and opposite angles of a cyclic quadrilateral add up to 180°. A tangent meets the radius at its point of touching at 90°.

Three questions to ask

There is no one right wording. Listen for the idea.

1. On the same arc, how do the angle at the centre and the angle at the circumference compare?
2. Why is the angle in a semicircle always 90°?
3. Why must a tangent be at a right angle to the radius where it touches the circle?

After the chapter, the learner can

• Use the rule that the angle at the centre is double
• Find angles in a semicircle and in a cyclic quadrilateral
• Use the rule that a tangent meets a radius at 90°