Suppose we try to find the circumradius of a triangle , as shown below: How can we find it? Note that the triangle is isosceles, with the equal sides being radii of the circumcircle. To find these, we only need to know the angle and side length AC. Angle intercepts the arc , with O at the center of the circle. Angle also intercepts the same arc, but with point B on the circumference of the circle. This means (1)…
Fun Facts about Pentagram Do you know that sum of all angles of a pentagram whose all five sides are extended to meet at five points is ? For example, sum of all angles , , , and in below figure of a pentagram is equal to . Proof: It is easy to prove that: (1) (2) (3) (4) (5) Let’s say sum of all angles from to is S. Adding all five equations (1)…
Calculating value of the Golden Ratio Introduction: The Golden Ratio, represented by Greek letter “phi” () exists when a line is divided into two parts and the longer part (b) divided by the smaller part (a) is equal to the sum of (a) + (b) divided by (b), which both equal 1.618. See diagram below where (1) Proof: Suppose is the ratio such that , where b > a For convenience, let’s set a = 1, so solving for…