In the following figure if \(A(\text{P -- ABC}) = 154\) cm2, radius of the circle is 14 cm, find : (a) \(m\angle APC\), (b) \(l(\text{arc } ABC)\).[Figure: circle with centre P; A at the bottom of the circle, C at the right of the circle, B on the ar…

Answer: (a) \(m\angle APC = 90^\circ\); (b) \(l(\text{arc } ABC) = 22\) cm

(a) Area of sector P–ABC \(= \dfrac{\theta}{360} \times \pi r^2\) (take \(\pi = \dfrac{22}{7}\))

\(154 = \dfrac{\theta}{360} \times \dfrac{22}{7} \times 14^2 = \dfrac{\theta}{360} \times 616\)

\(\theta = \dfrac{154 \times 360}{616} = 90^\circ\), so \(m\angle APC = 90^\circ\).

(b) \(l(\text{arc } ABC) = \dfrac{\theta}{360} \times 2\pi r = \dfrac{90}{360} \times 2 \times \dfrac{22}{7} \times 14 = \dfrac{1}{4} \times 88 = 22\) cm.