6.6.2 Angles and Tangents of Circles, PT3 Practice - Mathematics

6.6.2 Angles and Tangents of Circles, PT3 Practice

Question 4:

Diagram below shows a circle with centre O. POR is a straight line.

Find the value of x and of y.

Solution:

\begin{matrix} x = 40 \times 2 = 80 y = \frac{180 - 80}{2} = 50 \end{matrix}

$\begin{array}{l} x = 40 \times 2 \\ = 80 \\ y = \frac{180 - 80}{2} \\ = 50 \end{array}$

Question 5:

Diagram below shows a semicircle ABCD with centre O.

It is given that AB = CD.

Find the value of y.

Solution:

y^o+ 32^o + 32^o + 90^o = 180^o

y^o= 180^o – 154^o

y^o= 26^o

y = 26

Question 6:
In diagram below, ABC and DEF are straight lines.

Find the value of x and of y.

Solution:

$\begin{array}{l} x + 38 = 93 \\ x = 93 - 38 \\ x = 55 \\ ∠ D B G = 38^{o} (G B = G D) \\ y^{o} = ∠ D B G \\ ∴ y = 38 \end{array}$