1. Circle theorem 3 and

2. Find the unknown angles giving reasons for your answers.B
84o xo
Example Questions 1
Find the unknown angles giving reasons for your answers. yo 2
35o
angle x =
angle y =
41o (Angle at the centre).
75o(Angle at the centre)

3. Th3 Angles subtended by an arc or chord in the same segment are equal.
Theorem 3 yo xo xo
Th3

4. Angle x = 30o Angle x = angle y = 38o Angle y = 40o 38o xo yo 30o 40o
Angles subtended by an arc or chord in the same segment are equal.
Theorem 3
Find the unknown angles in each case
Angle x = angle y = 38o
Angle x = 30o
Angle y = 40o

5. Angles in the same segment
Drag the points around the circumference of the circle to demonstrate this theorem.
Hide one of the angles, modify the diagram and ask pupils to calculate the size of the missing angle.

6. Th4 The angle between a tangent and a radius is 90o. (Tan/rad)
Theorem 4 o
Th4

7. The angle between a tangent and a radius is 90o. (Tan/rad)
Theorem 4 o

8. 180 – (90 + 36) = 54o Tan/rad and angle sum of triangle.
If OT is a radius and AB is a tangent, find the unknown angles, giving reasons for your answers. T o
36o xo yo zo
30o A B
angle x =
angle y =
angle z =
180 – ( ) = 54o Tan/rad and angle sum of triangle.
90o angle in a semi-circle
60o angle sum triangle