Page 129 - Mathematics_Form_3

Circles

3. Using a protractor, measure the Theorem 5.1 is described as follows:
̂
angles formed on the circumference In the following figures, A O B is the angle
and at the centre of the circle. subtended by arc AB at the centre. Also,
̂
4. Comment on the relationship A X B is the angle subtended at point X on
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between the angles measured in the circumference of the circle. Applying
task 3. angle at the centre theorem,
̂
̂
A O ​B = 2A X ​B .
5. Using a pair of compasses, ruler,
and protractor, draw a similar Case I
shape and measure the central
X
angle and the angles formed on the
circumference.

6. Compare the results in task 3 and
task 5 to discover the relationship. O B
7. Write a general rule for the
relationship you have discovered.
A
8. Share your findings with other
students for further discussion. Case II
The general rule you have discovered
in Activity 5.4 is the central angle
theorem of circles. Generally, the angle
subtended by an arc at the centre of a O
circle is twice the angle subtended by X
the same arc at the circumference. This A B
result is useful in solving numerous
Mathematics for Secondary Schools The following is the statement of the Case III X O
angle problems related to circles and it
is known as angle at the centre theorem.

theorem.

Theorem 5.1

The angle which an arc subtends at
the centre of a circle is twice the angle
A
which it subtends at any point on the
remaining part of the circumference.
B

122 Student\s Book Form Three

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