learn maths with Eds
Given the lengths of the sides of a triangle, how to find the lengths of the medians? There are several formulae for determining the lengths of the medians. They are easily derived by applying Stewart’s Theorem. Stewart’s Theorem Let ABCRead More
Suppose that a quadrilateral ABCD be given with the following lengths of sides: AB = 3 cm, BC = 8 cm, CD = 6 cm and AD = 5 cm. (See Figure 1.) What is the radius of the circumcircleRead More
In this article, we’ll learn how to determine the equation of the bisector of the angle between two lines whose equations are given. For example, suppose that the equations of lines g and h are and , respectively. As FigureRead More
Every line in the Cartesian plane can be expressed in the general form Ax + By + C = 0. Suppose that the lines g and h have equations A1x + B1y + C1 = 0 and A2x + B2yRead More
In the article The Equation of The Polar of A Point with Respect to A Circle (1), it is shown that the equation of the polar of the point K(x1,y1) with respect to the circle (x – α)2 + (yRead More
This post introduces the concept of polars. There are several approaches to understanding the concept. The approach adopted in this article is through the points of tangency on a circle. [Regarding the notion of the points of tangency, the readersRead More
In the previous post The Equations of The Tangent Lines to A Circle (1), it is discussed how to determine the equations of the tangent lines to a circle on condition that the slopes of the lines are given. Now,Read More
If a line and a circle are placed on a plane, there are three possibilities in terms of the number of points of intersection between them. First, the line intersects the circle at two distinct points. (See Figure 1 below.)Read More
While the article The Centroid of A Triangle explains how to find the centroid of any triangle, this article elaborates on how to determine the centroids of some special-typed triangles, that is isosceles, equilateral, and right-angled triangles. The CentroidRead More
Suppose that ∆ABC is any triangle. To determine its centroid, draw the median passing through one of its vertices, A. Let D be the midpoint of the line segment BC. (So the median passes through A and D.) Similarly, drawRead More