1. Circle theorem 5 and 6

2. Introduction

3. The Alternate Segment Theorem.
The angle between a tangent and a chord through the point of contact is equal to the angle subtended by that chord in the alternate segment.
45o xo yo
60o zo
Find the missing angles below giving reasons in each case.
angle x =
angle y =
angle z = xo yo yo xo
45o (Alt Seg)
60o (Alt Seg)
Th5
75o angle sum triangle

4. Find angle ATS and angle TSRB
TSR = 70 T 70 R 80 A 70 S

5. Find angle ATS and angle TSRB
TSR = 70 T 70 80
ATS = 80 R 80 A
Set the pupils some examples to do. 70 S

6. Cyclic Quadrilateral Theorem.
The opposite angles of a cyclic quadrilateral are supplementary. (They sum to 180o) w y
Th6 r p x z s q
Angles x + z = 180o
Angles p + r = 180o
Angles y + w = 180o
Angles q + s = 180o

7. Find the missing angles below given reasons in each case.
Cyclic Quadrilateral Theorem.
Theorem 6
The opposite angles of a cyclic quadrilateral are supplementary. (They sum to 180o)
85o
110o x y
70o
135o p r q
Find the missing angles below given reasons in each case.
angle x =
angle y =
angle p =
angle q =
angle r =
180 – 85 = 95o (cyclic quad)
180 – 135 = 45o (straight line)
180 – 110 = 70o (cyclic quad)
180 – 70 = 110o (cyclic quad)
180 – 45 = 135o (cyclic quad)

8. Angles in a cyclic quadrilateral
Drag the points around the circumference of the circle to demonstrate this theorem.
Hide some of the angles, modify the diagram and ask pupils to calculate the sizes of the missing angles.

9. Start the clip at 2.32 mins