【Haichuan Teahouse】Brain-teaser Series: Determining the Area of a Circle with Three Squares
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Inside a circle, three squares of different sizes are stacked, as shown in the figure. Determine the area of the circle based on the lengths of the segments given in the figure.
Simplify the problem to an isosceles trapezoid with a height of 36, an upper base of 6, and a lower base of 18, and find the radius of its circumcircle. Its center is the intersection of the perpendicular bisectors of the two sides. ;P
It is understandable that there is an axis of 6+12+18 in the middle, but are the heights of the tangents from the small and large squares to the outer circle the same?
This post was last edited by Yang Qing on 2021-10-27 at 13:05; it’s different
As shown in the figure above: It is correct to use the intersection point of the perpendicular bisectors of the two waists as the center of the circle.