Math CentralQuandaries & Queries


Question from Mercede, a student:

there is a circle inside a square... there is a shaded rectangle that measures 5mm X 10mm and they want to know what the radius is. The edge of the shaded rectangle touches a point on the circle.

Hi Mercede,

I redrew the diagram you sent and added some lines and dimensions.


I let the radius of the circle be r mm and I drew a line segment from the centre of the circle to the point where the rectangle touches the circle. The length of this line segment is r mm. I then constructed a right triangle with this line segment as the hypotenuse. What does Pythagoras' theorem tell you about this triangle?


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