SPM Practice (Short Questions)

8.4 Circles, SPM Practice (Short Questions)

Question 9:

In figure above, ABC is a tangent to the circle centre O at B. AED is a straight line.

Find the value of y.

Solution:

∠ABO = 90^o

∠BOE = 2 × 40^o= 80^o

In quadrilateral AEOB,

∠AEO = 360^o– ∠ABO– ∠BOE – 35^o

= 360^o– 90^o – 80^o – 35^o= 155^o

y^o+ ∠AEO = 180^o

y^o+ 155^o = 180^o

y^o= 180^o– 155^o

y^o = 25

Question 10:

In figure above, ABC is a tangent to the circle centre O, at point B.

The value of x is

Solution:

∠OBC = 90^o

∠BOD = 2 × 50^o= 100^o

In quadrilateral BODC,

x^o= 360^o– ∠BOD – ∠OBC – 120^o

= 360^o– 100^o – 90^o – 120^o

= 50