Tangents A tangent is a straight line which touches the circle at a point but does not cut through the circle. There are two theorems involving tangents.

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 ...

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 ...

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 ...

The theorem concludes that the line containing the radius through the point of contact is also sometimes called the ‘normal’ to the circle at the point. Length of the tangent - The length of ...

(D) √119 cm Sol. We know that the line drawn from the centre of the circle to the tangent is perpendicular to the tangent. And so, ∴ OP ⊥ PQ By applying Pythagoras theorem in ΔOPQ, ∴OP² ...

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 ...

Solution: All 4 vertices touch the circumference of the circle. Using theorem 4. Opposite angles in a cyclic quadrilateral add up to 180° a = 180 – 60 = 120° b = 180 – 140 = 40° ...