Category: Geometry

I had to dig for a bit to find a complete proof for each part of the Power of a Point Theorem, so I thought it would be useful to compile my own proof. The Power of a Point Theorem states: Given a point P and a circle C, any line through P that intersects…

The topic in my geometry class today involved finding solutions to quadratic equations. The actual topic was on the ratio of lengths of secants in a circle, but that’s for another post. For a specific example, consider this problem. Two secants intersect outside a circle. The first secant line has segments of 15 (between the…

Terms For every polygon, there is a largest circle that fits entirely within that polygon. If that circle touches all sides of the polygon, then it is said to be inscribed; it is called the incircle, and its center is called the incenter (which is then also called the polygon’s incenter). Every triangle has an incenter…

Here’s a problem with an interesting solution. You’re given two triangles, T1 and T2. The sides of T1 are 25, 25, and 30. The sides of T2 are 25, 25, and 40. Which has the greater area? The impulsive answer is probably to say that T2 is larger, since the third side is larger. However,…

This is the formula for the circumference of a circle: \[C = 2\pi r\] It’s very simple. My recollection of how it was taught is as a mystical relationship between \(\pi\) and the circumference, as if it were some magical truth that \(\pi\), of all numbers, would be the number that would satisfy the need…

I recently read John Derbyshire’s book, Unknown Quantity: A Real and Imaginary History of Algebra (Plume 2007 edition). I recommend it overall, although the second half becomes increasingly inaccessible to the layperson. One bit that particular stuck in my head, because of the way it caused me to rethink a mathematical concept, was this passage…