Page 161 - Mathematics_Form_3

Circles

5. Prove that if two tangents are drawn
X
from an external point to a circle,
then they subtend equal angles at
the centre.
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Angles in alternate segments
Y
In Figure 5.24, the chord ‾ AB divides Figure 5.26: An angle formed in another
the circular region into two segments. In (alternate segment)
̂
Figure 5.25, A X B is in the first segment Activity 5.16 enables you to learn the unique
̂
while in Figure 5.26, A Y B is in the relationship between angles formed in
second segment (or alternate segment). alternate segments.
An angle subtended in the alternate
segment by a chord which forms another Activity 5.16: Deducing the
angle with a tangent at point of contact relationship between angles
have a unique relationship. formed in alternate segment and

angle between the chord and a
tangent.

First segment Individually or in a group, perform the
following tasks:
A B
Second segment 1. Draw a circle with centre O of any
convenient radius.
2. Draw a chord anywhere on the
Mathematics for Secondary Schools O X 4. Draw a tangent line in such a way
circle.
Figure 5.24: Two segments of a circle
3. Label from outside the circle, the
two segments formed.

that a point of contact is at one end
of the chord.
5. Identify and label the angle formed

Y
Also, identify the segment where
the angle you have labelled lies.
Figure 5.25: An angle formed in one between the chord and the tangent.
segment
6. Measure the angle you have labelled
in task 5.

154 Student\s Book Form Three

18/09/2025 09:59:53
MATHEMATIC F3 SB.indd 154
MATHEMATIC F3 SB.indd 154 18/09/2025 09:59:53