Monthly Archives: October 2022

MathCounts Geometry Exercise – 1

Posted on October 28, 2022 by kevin

25 20 30 ________ One rectangle is divided into four smaller rectangles. The areas of three smaller rectangles are $25\ cm^2$, $20\ cm^2$, and $30\ cm^2$ respectively, as shown in the diagram. Find the area of the shaded region (unit: … Continue reading →

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Distance between the incenter and circumcenter

Posted on October 7, 2022 by kevin

The distance between the incenter and circumcenter of a triangle, is calculated by Euler’s theorem in geometry: $$d=\sqrt{R(R-2r)}$$ which also implies $$R\ge2r$$ For a Bicentric quadrilateral, the distance between the incenter and circumcenter can be calculated by Fuss’s theorem or … Continue reading →

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