Page 157 - Mathematics_Form_3

Circles

Tangent properties of circles Theorem 5.10
In the previous sections, you learnt The angle between a tangent to the
about properties of angles and chords circle and the radius at the point of
of a circle. In this section, you will learn contact is a right angle.
the tangent properties of a circle. Engage
FOR ONLINE READING ONLY
in Activity 5.14 to learn the tangent Theorem 5.10 is described geometrically
properties of a circle.
as follows.
In Figure 5.22, the line segment AT is a
Activity 5.14: Deducing the nature tangent which touches the circle at point
of the angle formed by radius of A and ‾ OA is its radius.
a circle and a tangent at the point
of tangency

Individually or in a group, perform the O
following tasks:
1. Draw a circle of any convenient
radius with centre at O .
2. Draw a tangent to the circle and A T
label the point of contact by X.
Figure 5.22: Tangent of a circle
3. Join the points O and X by a line
segment OX to form a radius. According to Theorem 5.10, since the
tangent and radius meet at point A on the
4. Measure the angle formed between
the radius and the tangent. circle, then angle OAT in Figure 5.22 is
a right angle.
Mathematics for Secondary Schools 6. What is your observation about the properties of tangents from a point
5. Repeat tasks 1 to 4 by using two
Engage in Activity 5.15 to explore the
more circles with different radii.

outside a circle.
angles you have measured?
7. Write a general statement regarding
Activity 5.15: Deducing properties of
what you have discovered about
these angles.
tangents from a point outside a circle
8. Share your findings with other
Individually or in a group, perform the
students for further discussion.
following tasks:
1. Use a pair of compasses to draw
In Activity 5.14, the correct observation a circle with centre at O of a
is summarized in the following theorem. convenient radius.

150 Student\s Book Form Three

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MATHEMATIC F3 SB.indd 150 18/09/2025 09:59:51
MATHEMATIC F3 SB.indd 150