CIRCLES IN ORBITS

The length of segment $OA$ is $8\; meters$ .

The circles are in an orbit. Looking at the figure above, the circle $O_1$ is in orbit 1, circle $O_2$ is in orbit 2 and circle $O_3$ is in orbit 3.

1. Find the radius of circle $O_1$ and write its equation. $(10\; points)$
2. Find the radius of circle $O_2$ and write its equation. $(2\; points)$
3. Find the radius of circle $O_3$ and write its equation. $(2\; points)$
4. Find the radius of circle $C_2$ and write its equation. $(2\; points)$
5. Find the radius of circle $C_3$ and write its equation. $(2\; points)$
6. Find the radius of circle $C_4$ and write its equation. $(2\; points)$
7. From the results above, find a relationship between the radius of a given circle and that circle’s orbit number.
Write down a function of the radius with the orbit number as a variable. $(20\; points)$
8. What is the orbit number from which the radius is less than 0.2 millimeters. $(10\; points)$
9. Find the value of the blue shaded area. $(40\; points)$
10. Find the value of the brown shaded area. $(10\; points)$

$PS.\;All\; calculations\; will\; be\; done\; to\; the\; hundred\; thousandths$

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CIRCLES IN ORBITS

CIRCLES IN ORBITS

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