# GeoGebra

In this entry, I’m going to start with a concrete problem and develop an abstract generalization. The starting problem: Given isosceles trapezoid $$ABCD$$ with an altitude of 6. Point $$E$$ is on $$\overline{DC}$$ such that $$DE = 3$$, $$EC =… ## Constructing a Tangent I was recently asked for an elegant proof of the following problem. It’s based on a construction challenge from Euclidea. Given: Circles A, B, and C, such that point C is on circle A, point B is on circles A… ## Inscribing an Equilateral Triangle I was reminded of the cylindrical wedge that casts shadows of a triangle, a square, and a circle, and it got me wondering: What if I wanted to create such a shape with an equilateral triangle as one of its… ## The Free Throws Problem At a recent workshop on collaboration, the other participants and I were presented with a version of this problem: Adam hits 60% of his free throws. He gets fouled just before the buzzer, and his team is down by one… ## Isosceles Triangles in a Quadrilateral In this post, I’ll discuss two issues. First, I’ll look at a problem taken from a major textbook, and explain why the solution is wrong. Then, I’ll discuss why this particular problem bothers me in the greater context of mathematics… ## Polygon Sets: Doing the Math In my previous post, I created sets of regular polygons in GeoGebra by setting a parameter of the polygons equal to a constant. In this post, I will show the mathematics for determining the side length given a particular parameter…. ## Polygon Sets I recently found myself creating a set of regular polygons for a worksheet. I used GeoGebra to create them, and then free-handed the zoom in order to get them consistently sized. This led me to wonder what “consistently sized” would… ## SSA Congruence: Constraints In my last post, I pointed out that SSA is in fact sufficient for determining all three sides and angles under certain conditions. In this post, I will specify those conditions, with illustrations. Given two noncollinear segments \(\overline{S_1}$$ and $$\overline{S_2}$$…

I’m exploring if it’s possible to create a function in GeoGebra that would take an integer as input and create a simplified radical as output. For instance, it would take $$20$$ as input and return $$2\sqrt{5}$$ as output. I don’t…
Introduction In my previous post, I included this image, which I’d made in GeoGebra. The image satisfies the conditions of the problem: $$AD$$ is tangent to $$\odot P$$ and $$\overline{BC} \cong \overline{AD}$$. In order to create this image, I…