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The equation of a circle is: (x  h)^{2 } + (y  k)^{2 } = r^{2 } where (h, k) is the center of the circle. So if we can determine the equation of the circle, we can determine its radius. Let's start by putting the origin in the bottom lefthand corner. Then the center is (r, r), so we have (x  r)^{2 } + (y  r)^{2 } = r^{2} What's the location of the corner of the yellow rectangle where it touches the circle? It is (2, 1). So we can substitute that value of (x, y) into the circle's equation:
Lori, can you finish the problem from here? Hope this helps, Hi Lori, When I read your question I didn't understand it but Sue did. When I read Sue's solution I saw another way to approach it so I took her diagram, added two lines and labeled three points.
Lori wrote back.
Hi Lori. Yes, one of the solutions to the equation is 1, but that doesn't fit the diagram. However, it does fit most of the Can you see that this fits the description? That's why the value 1 works. However, for the diagram as I've drawn it earlier, there must be another solution, and there is. Does r = 5 work? Stephen La Rocque> Lori. In my diagram the triangle CAB is a right triangle and hence you can apply Pythagoras' theorem. If the length of the side AB is a, the length ofthe side BC is b and te length of the side CA (the hypotenuse) is c then Penny  


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