Page 160 - Mathematics_Form_3

Circles

⇒ y + 2 14y + 49 = y + 2 225 and that of the circle with centre

⇒ 14y = 176 B is R cm, show that the distance
between A and B is (r + R ) cm in
y = 12.6cm figure (a) and (R − r) cm in figure
But, (b).
FOR ONLINE READING ONLY
XY
tan x =
OY
15 A P B
tan x =
12.6
Thus,

x = tan − 1   15   = 50° T
 12.6  (a)

Hence,
z = 180°− (50°+ 90 )° = 40° (sum of

interior angles in triangle). P A B
Therefore, x = 50 , y° = 12.6cm and
z = 40 .°

(b)
Exercise 5.11
3. Suppose ‾ TA and ‾ TB are tangents
1. In the following figure, O is the centre from an external point T to a circle
of the circle inscribed in ΔABC. If with centre O. If A T O = 35° , find
̂
̂
̂
B A C = 50° and A B C = 70°, find A O B.
̂

the value of x .
A 4. In the following figure, the three
sides of the triangle ABC are
tangents to the circle at X, Y, and
B Z. If ‾ BX = 5 cm , ‾ CY = 3 cm and
O Mathematics for Secondary Schools
x ‾ AZ = 4 cm, find ‾ AX, ‾ BY , and ‾ CZ .
A

X

Z
C
2. In the following figures, the radius B Y C
of the circle with centre A is r cm

Student\s Book Form Three 153

18/09/2025 09:59:53
MATHEMATIC F3 SB.indd 153 18/09/2025 09:59:53
MATHEMATIC F3 SB.indd 153