First, find m, the gradient of the tangent. On a diagram, draw the circle and the tangent at the point P (3, -4) and draw the radius from the centre (0, 0) to the point P.

Monash University researchers have extended Descartes’ Circle Theorem by finding a general equation for any number of tangent circles, using advanced mathematical tools inspired by physics. A ...

Descartes’ theorem, a cornerstone of geometry, defines the relationship between four mutually tangent circles. But for centuries, generalizing the equation to more than four circles had eluded ...

A Steiner chain of length k consists of k circles tangent to two given non-intersecting circles (the parent circles) and tangent to each other in a cyclic pattern. The Steiner porism states that once ...

Graphs of Sine and Cosine 1.2 An applet illustrating how the graphs of sine and cosine are related to the unit circle. Transformations of Functions 1.3 An applet illustrating how transformations ...

In this paper we propose a remote password authentication scheme based on a circle. This scheme is simple and practically feasible in a multi-server environment. In this scheme, we use some simple ...

First, find m, the gradient of the tangent. On a diagram, draw the circle and the tangent at the point P (3, -4) and draw the radius from the centre (0, 0) to the point P.