6.7.3 Angles and Tangents of Circles, PT3 Focus Practice - Mathematics

Question 7:

In figure above, ABCD is a tangent to the circle CEF at point C. EGC is a straight line. The value of y is

Solution:

\begin{array}{l} ∠ C E F = ∠ D C F = 70^{\circ} \\ ∠ A E G + 70^{\circ} + 210^{\circ} = 360^{\circ} \\ ∠ A E G = 80^{\circ} \\ In cyclic quadrilateral A B G E, \\ ∠ A B G + ∠ A E G = 180^{\circ} \\ y^{\circ} + 80^{\circ} = 180^{\circ} \\ y = 100 \end{array}

Question 8:

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