how to calculate the partial area of a circle given its radius?

Question

how to calculate the partial area of a circle given its radius?

Given: radius $r$ and two axis coordinates. Find areas $A$, $B$, $C$ and $D$

Answer 1

You can always use integration. But if you want, you can always use geometry and algebra

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You can always break the parts down into sectors and triangles. In the first quadrant, the area can be expressed as: $$A_{Q1}=A_{\text{sector}ADC}+A_{\triangle DIH}-A_{\triangle HAC}$$

The areas can be easily worked out if you just have the center $(h,k)$ and $r$ in the equation for your circle: $(x-h)^2+(y-k)^2=r^2$.

You can repeat the process for the rest of the quadrants, adding and subtracting areas as necessary.

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For $Q2$:

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For $Q3$:

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For $Q4$: