MHB Measuring Hollow Sphere Diameter with Compass & Ruler

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To measure the diameter of a hollow sphere using only a compass and a ruler, first, draw a circle on a flat surface that represents the sphere's cross-section. Use the compass to find the radius by placing the point on the center and drawing a circle. Measure the radius with the ruler, then double this measurement to find the diameter. Ensure that the compass is accurately placed at the center for precise results. This method provides a straightforward way to determine the diameter without advanced tools.
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Using only a compass and a ruler, how can we measure the diameter of a hollow sphere?
 
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jmprada said:
Using only a compass and a ruler, how can we measure the diameter of a hollow sphere?

Hi jmprada! ;)

Here's my attempt.

We use the ruler to draw a straight line on the inside of the sphere.
The line will go all the way round and form a great circle.
Repeat and draw a second great circle.
Those 2 great circles will intersect each other in 2 points.
Measure the distance between those 2 points and we have the diameter.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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