# 6.7.3 Angles and Tangents of Circles, PT3 Focus Practice

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:
$\begin{array}{l}\angle CEF=\angle DCF={70}^{\circ }\\ \angle AEG+{70}^{\circ }+{210}^{\circ }={360}^{\circ }\\ \angle AEG={80}^{\circ }\\ \\ \text{In cyclic quadrilateral}ABGE,\\ \angle ABG+\angle AEG={180}^{\circ }\\ {y}^{\circ }+{80}^{\circ }={180}^{\circ }\\ y=100\end{array}$

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 = 90o
BOE = 2 × 40o = 80o