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Monday, March 7, 2016

Old, Old Favorite


Below, a problem I gave to a local math meetup group some weeks back thinking it would be familiar to EVERYone (it is my favorite problem from geometry class that I had 50 years ago(!), and I've seen it on the Web multiple times). To my surprise, NO ONE was familiar with it, so I present it here in case anyone else has led such a sheltered life as to have missed this delightful puzzle ;-):

MNOP is a RECTANGLE inscribed in one quadrant of a circle ("O" being the origin/center of the circle).
PO = 10 cm.
SP= 3 cm.

What is the length of diagonal line PN?
(solution can be arrived at in seconds with no trig and very little geometry required)
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ANSWER:  as a diagonal, PN is EQUAL to MO (not drawn in). MO is a radius, as is SO. SO=13, thus PN=13.


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