S3 BLOCK 8 Angles and Circles I can find the size of a missing angle using the following facts. Angle in a semi circle. Two radii and a chord form an isosceles triangle. The tangent and the radius. 1

Angle in a semi-circle When a triangle is drawn in a semi-circle, the angle on the circumference is always a right angle.

Example 1: find the angles marked with letters. O, is the centre of the circle.

Example 2: find the angles marked with letters. O, is the centre of the circle.

Two radii When the ends of a chord are joined to the centre of a circle, an isosceles triangle is formed. The two angles marked are equal.

Example 1: find the angles marked with letters. O, is the centre of the circle.

Example 2: find the angles marked with letters. O, is the centre of the circle.

The tangent and the radius A tangent is a line that touches only one point on the circumference of a circle. A tangent is always perpendicular to the radius of the circle. That is, the angle between the tangent and the radius is 90° at the point of contact.

Example: find the angles marked with letters. O, is the centre of the circle