Math Puzzle of the Week

June 15, 2009

Graph Theory: There are 5 people at a party. Is it possible for each person to shake hands with 3 other people?

Math Factor podcast

Answer available June 22, next puzzle

Answer to math puzzle of June 8:

Geometry: Two tangents to a circle form a 72° angle. What is the size of each arc between the tangent points?

From NCTM

Solution: By constructing radii from the tangent points, we have a quadrilateral, the sum of whose internal angles is 360°. The angles at the tangent points is 90°, of course, so that leaves 108° for the central angle, the same as the arc size, and the other arc is 252°.

For more math puzzles, check out http://www.mathpuzzle.com/, http://mathschallenge.net/, http://www.princeton.edu/~mathclub/puzzles4.html and http://mathforum.org/k12/k12puzzles/

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updated 16 June 2009
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