Circle in the Square
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Refer to the diagram above.
Assume that we have a perfect circle inside a square. The square is just large enough so that the
circumference of the circle touches the square on each side at one point.
In one corner of the square, we have a rectangle, which shares a corner with the square and touches the
circumference of the circle at only one point.The length of the rectangle is 12 cm, and its width is 6 cm.
What is the radius of the circle? Please include the details of your solution with your answer. Incidentally,
we will enforce Charles Weidig’s First Rule of Geometry: “Never trust a diagram”. In other words, taking
measurements is not an acceptable means of solution, since the diagram is for illustrative purposes only
and may not be dimensionally correct.
DOTHEMATH.
Submit your answers to:
Discover Smith Mountain Lake Magazine
P.O. Box 880
Moneta,VA 24121
Or via e-mail to:
editor@discoversmithmountainlake.com
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O ces in:
SALEM, VINTON, ROANOKE,
SMITH MOUNTAIN LAKE
and the NEW RIVER VALLEY
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“
You and I both know… this is BEYOND
ridiculous…”
“
OK, I admit it – I’m a copy cat.”
“
Just so you know…I’m fine being left at home alone.”
The first reader to submit a
correct solution will be featured
in the next issue of Discover
Smith Mountain Lake.
“
Who let the cat out of the bag?”
Discover Smith Mountain Lake |
www.discoversmithmountainlake.com
Discover Smith Mountain Lake | Spring 2013
25
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A Brain Teaser