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Problem

The arbelos consists of three points $A,B$ and $C$ which are collinear, together with the semicircles $ADB$, $AXC$ and $CYB$ as shown in Figure 1. In the figure $\overline {CD}$ has been added to the figure tangent to the two small semicircles. $\overline {AD}$ intersects a small semicircle at $X$ and $\overline{BD}$ intersects the other small semicircle at $Y$. $\overline{XY}$ intersects $\overline{AD}$ at $P$. Prove the area of the arbelos is equal to the area of the circle with diameter $\overline{CD}$, $\overline{XY}$ and $\overline{CD}$ bisect each other, and $\overline{XY}$ is tangent to the small semicircles.

Details
Contributer: Tom R
Source Title: BMC Talk
Authors
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References
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Problem Sets This Problem Belongs to:
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VARIABLES
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DEFINITIONS
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