6.5.2 Common Tangents (II) - Mathematics

6.5.1 Common Tangents (II)

3. Do not intersect

(a) Circles of the same size

Number of common tangents	Properties of common tangents
Four common tangents: AB, CD, PS and RQ	AB = CD = OV PS = RQ AB // OV // CD

(b) Circles of different sizes

Number of common tangents	Properties of common tangents
Four common tangents: AB, CD, PS and RQ	AB = CD BT = DT PS = RQ OA // VB OC // VD

Example 1:

In the diagram, ABG and 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 × 56^o = 28^o

angle FBG = 90^o ← (tangent is 90^o to radius)

x^o+ 28^o + 90^o = 180^o

x^o= 180^o – 118^o

x^o= 62^o

x = 62

(b)

angle AOF = x^o = 62^o← (AO// BF)

y^o= 2 × 62^o

y^o= 124^o

y = 124

(c)

Exterior angle of AOC = 360^o – 124^o = 236^o

Angle EOC = ½ × 236^o = 118^o

z^o= (180^o – 118^o) × ½ ← (∆ EOC is isosceles triangle, angle OEC = angle OCE)

z^o= 31^o

z = 31