8.1 Tangents to a Circle (Examples)

Example 1:

In the diagram, O is the centre of a circle. ABC and CDE are two tangents to the circle at points B and D respectively. Find the length of OC.

Solution:

OC²= OB² + BC² ← (Pythagoras’ Theorem)

= 6² + 8²

= 100

OC = √100 = 10 cm

Example 2:

In the diagram, AB and BC are two tangents to a circle with centre O. Calculate the values of

(a) x (b) y

Solution:

(a)

AB = BC

7 + x = 12

x = 5

(b)

∠

OBA =

∠

OBC = 21^o

∠

OAB = 90^o ← (OA is perpendicular to AB)

y^o= 180^o – 21^o– 90^o

y = 69

Example 3:

In the diagram, ABC is a tangent to the circle with centre Oat point B. CDE is a straight line. Find the value of x.

Solution:

∠

CBO = 90^o ← (OB is perpendicular to BC)

In ∆ BCE,

x = 180^o – 30^o– 50^o– 90^o

x = 10^o