Question

In the given figure, if A(P$-$ABC) = 154 cm² radius of the circle is 14 cm,

find
(1) $\angle$APC.

(2) l ( arc ABC) .

Answer 1

Radius of the circle, r = 14 cm

(1)
A(P$-$ABC) = Area of the sector PABC = 154 cm²

$$\begin{gathered} \therefore \frac{\theta }{360°}\times \mathrm{\pi }{r}^2=154 \\ \Rightarrow \frac{\angle \mathrm{APC}}{360°}\times \frac{22}{7}\times {\left(14\right)}^2=154 \\ \Rightarrow \angle \mathrm{APC}=\frac{154\times 7\times 360°}{22\times 196}=90° \end{gathered}$$
Thus, the measure of $\angle$APC is 90º.

(2)
l(arc ABC) = Length of the arc ABC $=\frac{\angle \mathrm{APC}}{360°}\times 2\mathrm{\pi }r=\frac{90°}{360°}\times 2\times \frac{22}{7}\times 14$ = 22 cm

Thus, the length of arc ABC is 22 cm.