Question

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

(1) `∠APC` 

(2) l ( arc ABC) .

Answer 1

The radius of the circle, r = 14 cm
(1) 
A(P-ABC) = Area of the sector PABC = 154 cm²

\[\therefore \frac{\theta}{360° } \times \pi r^2 = 154\]

\[ \Rightarrow \frac{\angle APC}{360° } \times \frac{22}{7} \times \left( 14 \right)^2 = 154\]

\[ \Rightarrow \angle APC = \frac{154 \times 7 \times 360° }{22 \times 196} = 90° \]

Thus, the measure of `∠`APC is 90º.

(2) l (arc ABC) = Length of the arc ABC 

\[= \frac{\angle APC}{360°} \times 2\pi r = \frac{90° }{360° } \times 2 \times \frac{22}{7} \times 14\]  = 22 cm

Thus, the length of arc ABC is 22 cm.