The triangle is one of the most frequently discussed geometric figures in the study of geometry. Its relationship with circles is fundamental to understanding various geometry results. Some of these results are called notable points of the triangle. Similarity of Triangles In the proportions post, we saw concepts of similarity of triangles. Here we will show that the similarity of triangles can be demonstrated by circles. Triangles inside the circle Lemma 1: Let AB and CD be different chords of a circle that intersect at a point P inside the circle. Then $$\dfrac{AP}{CP} = \dfrac{PD}{PB} $$
Learning about angles in circles is fundamental. This concept was extensively addressed by Euclid and the Greeks in general, such as Pythagoras and Archimedes. Bow Definition: Let $A$ and $B$ be points on a circle in a plane. The straight line $\vec{AB}$ (arc) separates the plane into two half-planes, each containing a part of the circle. Central Angle Definition: Let $A$ and $B$ be points of a circle on a center plane $C$. The central angle $\angle ACB$ determined by $A$ and $B$ or determined by the chord $AB$.
The main work on geometry, Euclid’s book Elements, has several results for straight lines and circles. In this post, we will show several results for this subject. Basic Settings Below we define some fundamental terms for working with circles. Center Definition (Center): is a point that is the same distance from any point on the circle. Ray Definition (Radius): is any straight line segment that runs from the center to the circumference.