8.3 Common Tangents (Sample Questions)


Example 1:
 
In the diagram, ABGand CDG are two common tangents to the circle with centres O and F respectively. Find the values of
(a) x,  (b) y,  (c) z.
 
Solution:
(a)
In ∆ BFG,
angle BFG= ½× 56o = 28o
angle FBG= 90o ← (tangent is 90o to radius)
xo+ 28o + 90o = 180o
xo= 180o – 118o
xo= 62o
x = 62
 
(b) 
angle AOF= xo = 62← (AO// BF)
yo= 2 × 62o
yo= 124o
y = 124

(c)
Exterior angle of AOC = 360o – 124o = 236o
Angle EOC = ½ × 236o = 118o
zo= (180o – 118o) × ½  ← (∆ EOC is isosceles triangle, angle OEC = angle OCE)
zo= 31o
z = 31

Leave a Reply

Your email address will not be published. Required fields are marked *