Circles Cover a Quadrilateral

Here is a problem from one of the first issues of the Russian Kvant magazine (G. Galperin, M10, n 2, 1970):

Four circles centered at the vertices of a quadrilateral ABCD completely cover the quadrilateral. Prove that some three of the circles cover one of the triangles ABC, BCD, CDA, DAB.

(In the applet you can click inside a circle to make it disappear or reappear again.)

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?

It is relatively easy to prove the statement by considering several cases. I find this messy and solicit more elegant solutions, which appears to escape me. Please post at the bottom of the page.

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