A-B-and-E-are-three-circles-all-with-radius-1-unit-A-and-E-touch-at-P-whole-B-and-E-touch-at-Q-POQ-x-where-O-is-the-centre-of-E-Find-the-area-of-the-overlapping-portion-of-A-and-B-if-0-x-60-

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Question Number 16570 by chux last updated on 24/Jun/17

$$\mathrm{A},\mathrm{B}\mathrm{and}\mathrm{E}\mathrm{are}\mathrm{three}\mathrm{circles}\mathrm{all}$$$$\mathrm{with}\mathrm{radius}1\mathrm{unit}.\mathrm{A}\mathrm{and}\mathrm{E}\mathrm{touch}$$$$\mathrm{at}\mathrm{P}\mathrm{whole}\mathrm{B}\mathrm{and}\mathrm{E}\mathrm{touch}\mathrm{at}\mathrm{Q}.$$$$\mathrm{\angle }\mathrm{POQ}=\mathrm{x}°\mathrm{where}\mathrm{O}\mathrm{is}\mathrm{the}\mathrm{centre}$$$$\mathrm{of}\mathrm{E}.\mathrm{Find}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}$$$$\mathrm{overlapping}\mathrm{portion}\mathrm{of}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{if}$$$$0⩽\mathrm{x}⩽60°$$

Commented by chux last updated on 24/Jun/17

$$\mathrm{pls}\mathrm{help}$$

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