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A circle with diameter 10 units sits atop a square so that the circle is tangent to the square at the center of the top side. The sides of the square are extended until they also are tangent to the circle as shown. The perimeter of the resulting figure can be written in the form m+n*pi units where m and n are integers. What is the value of m + n?

 Nov 21, 2022
 #1
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m + n = 44

 Nov 21, 2022
 #2
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It is 45 not 44. The three sides are 10+10+10 which equals 30. That is our first value and since the sides of the square go up to the diameter of the circle, we get 5+5. Now our sum so far is 40. Now we have a semicircle so we just find the circumference of that to get another 5. The numbers add up to 45.

Guest Nov 22, 2022

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