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Hexagonal Dilemma (Posted on 2004-06-02) Difficulty: 4 of 5
A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed in a circle. Find the radius of the circle.

As suggested, *if* it matters, you may assume that the sides listed are given in order

No Solution Yet Submitted by SilverKnight    
Rating: 4.0000 (5 votes)

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Solution here goes | Comment 14 of 18 |
assuming the sides are in the order given
(graph paper & compas help to visualize this)
the top and bottom of the hexagon are the sides with length 7
which are parallel.   Therefore you also have an inscribed
RECTANGLE of width 7, length unknown.   Draw a perpendicular
from the unknown length to the point where the 2 length side
touches the circle (either one)  You now have 2 right triangles,
1 with hypotenuse of 2, the other with hypotenuse of 11.
Use pythagorean theorem to get the unknown length of the
rectangle.  A third right triangle with hypotenuse from the center
of this rectangle to the point on the circle where 2 and 7 meet.
Its hypotenuse is the radius.  I get  sqrt 42   ~6.48
If I did this right, it seems to be more accurate since loss of
precision of all those nasty trig thingys.

  Posted by Steve Royer on 2004-06-04 20:08:16
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