Page 164 - Mathematics_Form_3

Circles

2 Solution
5. Calculate BT CT× and AT
From the figure, it follows that
6. Make a general statement of your PT QT× = XT (intersecting secant
2
findings.
and tangent)
FOR ONLINE READING ONLY
7. From the knowledge of congruency Thus,
and what you have learnt so far ( xx + 5) 6= 2
in circles, establish the general
⇒ x + 2 5x − 36 0=
formula.
9
4
Thus, x = − and x = .
8. Share the results with other students
Since, length cannot be negative
for further discussion.
Therefore, the value of x = 4cm .
In Activity 5.17, you have found that
2
BT CT× = AT . This fact is explained Example 5.26
in the following theorem.
In the following figure find the values

of x and y (all dimensions are in cm).
Theorem 5.13
D
When a secant and tangent intersect 12
3 E
at any external point the product
4 y C 8
of the lengths of the secant and its A F
external segment is equal to the x
square of the length of the tangent.
B
Solution
From the figure, it follows that
Example 5.25
DF FB AF FC× = × (intersecting
In the following figure, find the value chords)
of x . Thus,
4y = 3x Mathematics for Secondary Schools
P
Also;
2
AE CE× = DE (intersecting secant

5 cm
Q and tangent).
x Thus,
(y + 12) 8 12×= 2
T
X 6 cm ⇒ 8(y + 12) 144=

Student\s Book Form Three 157

18/09/2025 09:59:55
MATHEMATIC F3 SB.indd 157 18/09/2025 09:59:55
MATHEMATIC F3 SB.indd 157