1. Family Of Circle
By :
Murtadha Rafaai (0916063)
Nur Hakimi Bin Mat @ Ahmad ( 0914009)

2. Aims
• To show the following on a diagram of a
circle: radius, diameter, sector,
segment, chord and tangent.
• To introduce the circle theorems.
• To find unknown angles within a circle
and at tangents to circles using the
circle theorems.

3. Circle
Tangent
Circumference
Radius
Diameter

4. Angles subtended by the same
chord
Draw in a chord
Then draw two
triangles, using the
chord as a base, that
touch the
circumference.
Measure the angles at
the circumference.
What do you notice?

5. Angles subtended by the same
chord are equal
Chord

6. Angles subtended by the same
chord are equal
The chord is
not always
drawn in.

7. Angles subtended by the same
chord are equal
What is the
35 value of a?
a
a = 35

8. Angle at the Centre
Draw a triangle with all
the vertices touching the
circumference.
Draw another triangle
using the same base but
with a vertex at the
centre.
Measure the angle at the
circumference.
Measure the angle at the
centre.
What do you notice?

9. Angle subtended by the same
chord at the centre is twice
that at the circumference
a
2a

10. Angle subtended by the same
chord at the centre is twice
that at the circumference
Sometimes
you will have
a to spot the
property being
used.
2a

11. Angle subtended by the same
chord at the centre is twice
that at the circumference
What is the
value of angle
25 a?
50 2a = 180 – 50
a a 2a = 130
a = 65

12. Cyclic Quadrilaterals
Cyclic Quadrilaterals
•Draw a quadrilateral
with all four vertices
touching the
circumference.
•Measure opposite
angles and find their
sum.
What do you notice?

13. The opposite angles of a cyclic
quadrilateral add up to 180
a
A cyclic quadrilateral
is a quadrilateral
whose vertices all lie
on the circumference
of a circle.
b Angle a + angle b = 180○

14. Angles in a Semi-circle
Draw in a diameter.
Use this as a base to draw
a triangle with the vertex
at the circumference.
Measure the angle at the
circumference.
What do you notice?

15. Angle in a semi circle equal 90

16. Radius and Tangent
Draw in a radius
Draw a tangent meeting
the circle at the end of the
radius.
Measure the angle between
the radius and the tangent.
What do you notice?

17. The radius and tangent are at
right angles
o

18. The radius and tangent are at
right angles
o

19. The radius and tangent are at
right angles
o

20. The radius and tangent are at
right angles
o

21. The radius and tangent are at
right angles
o

22. Tangents to a Circle
Mark a point outside
of the circle.
Draw two tangents
to the circle from
this point
Measure the lengths
of the tangent from
the point to the
circle.
What do you notice?

23. Two tangents from the same
point to a circle are equal