Question

i need help on this question

Answer 1

Using the tangent relation,

$\begin{gathered} m\angle APB\text{ =}\frac{\text{ major arc - minor arc}}{2} \\ \text{Let the minor arc = x}^0 \\ \text{ Then, the major arc = 3x}^0 \end{gathered}$

The angles subtended by the major and minor arc sums up to 360 degrees.

$\begin{gathered} \text{ Therefore,} \\ 3x^{}+x^{}=4x \\ 4x\text{ = 360} \\ x=90^0 \end{gathered}$

That means, the angle subtended by the major arc

$=3\text{ }\times90^0=270^0$

While the angle subtended by the minor arc is

$90^0$

Applying the tangent relation above

$m\angle APB\text{ = }\frac{270-90}{2}=\frac{180}{2}=90^0$

Therefore, t