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Find the area of the circular section as shown in the figure
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| Photo by Math Principles in Everyday Life |
Solution:
If a small circle is tangent to the chord of a big circle, then the chord is bisected at the point of tangency. The radii of two circles are perpendicular to the point of tangency. To analyze more the problem, it is better to label further the figure as follows
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| Photo by Math Principles in Everyday Life |
Let R1 = be the radius of a big circle
R2 = be the radius of a small circle
If you connect the half of a chord and radii of two circles, then it becomes a right triangle. By Pythagorean Theorem, we can have the first working equation as follows
The area of a big circle is
.The area of a small circle is
.The area of the circular section is
Therefore, the area of the circular section is
