The Ermanometry Dynamic Template & Similar Right Triangles
Point B is the center of circle B.
BA and BE are radii of the circle.
AC is tangent to circle B at point A.
A tangent to a circle is perpendicular to a radius drawn to the circumference of the circle at the same point:
- Angle BAC is a right angle;
- Triangle ABC is a right triangle.
- Altitude AD is perpendicular to BC, creating right triangles ABD and ADC.
BC intersects the circumference of circle B at point E.
All three right triangles are similar.
In similar right triangles, the proportional relationships between the sides of any one triangle are the same for all the triangles.
The following graphic illustrates a few of the proportional relationships in similar right triangles:
The Inverse Of A Point Relative To A Given Circle
With the exception of the center, every point inside the circle has an inverse point outside the circle.
Every point outside the circle has an inverse point inside the circle.
Every point on the circle is its own inverse.
Point C outside circle B is the inverse of point D inside circle B.
Chord AE replaces arc AE.
Right triangle ADE is not similar.
Triangle ADE has significant proportional relationships to the three similar triangles. For example: AE squared divided by DE is twice AB, the diameter of circle B.
The 1962-1974-1982 moves, 3093 and 1981 days, are two known values.
This template shows 3093 on radius BA and 1981 on BD.
Two sides of triangle ABD are known, so all sides of all triangles may now be calculated.
The calculated value 4829.2 appears on BC.
The 1982-2001 move, 4829 days long, represents the distance from the center of circle B to point C outside the circle.