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Hart’s theorem says If a triangle be formed by the arcs of three circles, the inscribed and the three escribed circles are all tangent to a new circle or line. Here “triangle” mean...
This puzzle is an original. I have a solution to all parts but there may be better, more elegant, solutions out there and I know from past puzzles that some really, really good lat...
I ran across a geometry theorem with the following diagram. The theorem corresponding to the diagram is interesting, but I found reproducing the diagram more interesting. The segme...
You have a square with an inscribed circle as shown below. You want to draw a straight line such that the remaining part of the circle (in blue) and the remaining part of the squar...
This post will reveal the connection between my two previous posts: one on the Star Trek lemma and one on Pythagorean triples. In the process of writing the latter, I looked at the...
This is not an original, I saw it today (link given in spoilers - also shows solution, so really is a spoiler...) Squares, triangle and circle puzzle This puzzle was shown to me to...
The diagram shows five semicircles. The blue semicircles are congruent. Wherever things appear to touch, they touch. Wherever diameters appear to be horizontal, they are horizontal...
Take two concentric equilateral triangles of sizes k and 3n-k for 0 < k < 3n. Orient them in opposite directions, say up and down. Consider the shapes obtained by taking the...
You have an equilateral triangle and an inscribed circle. On each of the three sides, a point is randomly chosen (all points equally likely to happen). You connect each of the poin...
Uniformly random point P is chosen on a disk with diameter AB. What is the expectation of ∠APB? Express the answer as the sum of two numbers, in radians. Clarification: ∠APB is mea...
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