A regular 5-pointed star is composed of five lines, and has 5 non-overlapping triangles in it.
geometry/pentagram.ten.triangles New
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Problem
A regular 5-pointed star is composed of five lines, and has 5 non-overlapping triangles in it. Can you add two lines and increase the number of non-overlapping triangles to 10? -- Richard Gershbock <rtg@triple-i.com> (November 1995; "My kid got this problem in school.")
Show solution
.
x6.
. x
y . 5
. . . . . 7 y 8 . . x .4.
. 10 y .x draw a line connecting the x's.
. 9 y 3 x and a line connecting the y's and extend
. . . y then out til they meet.
. 1 . .2 . x=y
. . . .
. .
the numbers show the approximate places of the triangles.
-- Amy Jan Galitzer <panthera@wam.umd.edu>
It checks out. Thanks a bunch.
-- Richard Gershbock <rtg@triple-i.com>