Friday, June 25, 2010

Fox 293 - Solutions

According to the order of submission...
by Bob Ryden: (Ajit commented a very similar one)

by Bleaug:

Two tangents to a given circle define a symmetric 'kite' figure. By construction, the two kites defined by OUV and OTU are isometric because they have identical short legs. Since angles in T, U, V are right angles, blue and green angles are supplemental. Hence, angle a is angle(OUV). From Thales theorem we get cos(a) = 1/3

by Yu:
Several steps remain implicit in the figure. More words may be needed for a formal proof. But the solution holds.

by Binary Descartes:

Common tangents from the same point have equal lengths.
See the two identical deltoids (kites) sharing the same side.
Then cos(a) = e/3e = 1/3.

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