#### Question

In the given figure, if A(P-ABC) = 154 cm^{2 }radius of the circle is 14 cm, find

(1) `∠APC`

(2) l ( arc ABC) .

#### Solution

The radius of the circle, r = 14 cm

(1)

A(P-ABC) = Area of the sector PABC = 154 cm^{2}

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

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

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

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.

Is there an error in this question or solution?

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In the Given Figure, If A(P-abc) = 154 Cm2 Radius of the Circle is 14 Cm, Find (1) ∠ a P C (2) L ( Arc Abc) . Concept: Perimeter and Area of a Circle.

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