Question 756225: A square of area 40 cm2 is inscribed in a semicircle.
Find the area of the square that could be inscribed in a circle of the same radius.
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! I solved only halfway through, enough to get the radius and equation of the circle.
This would go better with a picture, but that was easier on paper than arranging it for the posting of a solution.
The inscribed square is 40 sq. units, so each side is  .
Using a graph with diameter of semicircle on x axis, the middle of the diameter on the origin, the semicirlce above the x axis;
Lower side is from -x to x. Left and right sides each are length y and  . Because we have a square figure, we can find on the graph,  .
EQUATION for CIRCLE is  and we wish to know r the radius.
 the radius.
That is as I say, only halfway through to your finished solution, meaning only halfway solved. Can you take the rest of the way? At least you know the radius of the circle and its equation.
TO CONTINUE, here is a big hint.
The square inscribed in circle, NOT simply the semi-circle, will have the same center as that of the circle. Since square, there are four triangles formed with the central angle of 90 degrees. RIGHT Triangles, each of them. Two sides of 5*sqrt(10). This is a special triangle. The 90-45-45 type. Height and base each are same measure as the radius of the circle and there are four of these triangles.
Area is (1/2){base}{height} and done four times.
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Final answer should be 125 square units. See how?
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