Page 154 - Mathematics_Form_3
P. 154
Circles
Intersecting chords 11. Write a general statements to
Two chords of a circle can intersect summarize your findings.
inside or outside the circle. Activity 12. Share your findings with other
5.13 engages you in recognizing students for further discussion.
properties of intersecting chords of a
FOR ONLINE READING ONLY
circle.
From Activity 5.13, you have learnt that,
if two chords intersect inside the circle,
Activity 5.13: Recognizing then the products of the lengths of the
properties of intersecting chords
of a circle segments of each chord are equal. If two
chords intersect outside the circle, then
Individually or in a group, perform the product of the lengths of the secant
the following tasks: and its external segment is equal to the
1. Draw a circle with any convenient product of the lengths of the other secant
radius with centre at O. with its external segment. This fact is
2. Draw two chords ABand CD explained in the following theorem.
so that they intersect inside the
circle at E. Theorem 5.9
3. Use a ruler to measure the lengths (a) When two chords intersect
of AE,BE,CE, and DE. inside a circle, the products of
the lengths of the segments of
4. Compute AE BE× and CE DE× . each chord are equal.
5. Write a general statement to (b) When two chords intersect
summarize your findings. outside the circle (secants), the
product of the lengths of the
6. Draw another circle with a
convenient radius. secant and its external segment
is equal to the product of the
7. Choose points P and Q on the lengths of the other secant
circle and another point R outside with its external segment. This
the circle. Mathematics for Secondary Schools
is referred to as; intersecting
8. Draw secant lines PR and QR, chords or intersecting secants.
mark the points S and T where the
lines intersect the circle. The theorem of intersecting chords
9. Use a ruler to measure the lengths can be proved using the concept of
of PR,RS,RQ, and RT. similarities.
10. Compute RS PR× and RQ RT.× Theorem 5.9 is described geometrically
as follows.
Student\s Book Form Three 147
18/09/2025 09:59:49
MATHEMATIC F3 SB.indd 147 18/09/2025 09:59:49
MATHEMATIC F3 SB.indd 147
