What does mutually tangent mean?

What does mutually tangent mean?

Circles are “mutually tangent” when each pair of them touch at a single point. At that point their common tangent will be perpendicular to the line that joins their centers.

What is Descartes circle Theorem?

Descartes’ circle theorem (a.k.a. the kissing circle theorem) provides a quadratic equation satisfied by the radii of four mutually tangent circles. By solving this equation, one can determine the possible values for the radius of a fourth circle tangent to three given, mutually tangent circles.

Who Solved the tangent line problem?

This understanding of limits, as well as the modern definition of continuity, were developed by Cauchy in the nineteenth century, well over a hundred years after Descartes and Fermat developed their methods to solve the tangent line problem.

What are three tangents?

Three tangents to a circle. Question: The three lines PS, PT, and RQ are tangents to the circle. The points S, X, and T are the three points of tangency.

How many tangents can 3 circles have?

Hence, a circle can have infinite tangents.

How do you draw a three tangent circle?

To construct the circles, form a triangle from the three centers, bisect its angles (blue), and drop perpendiculars from the point where the bisectors meet to the three sides (green). The points where these perpendiculars cross the sides are the desired points of tangency.

What is the circle theorem rule?

Circle Theorem. Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs. A circle is the locus of all points in a plane which are equidistant from a fixed point.

What are common tangents?

A line which is tangent to more than one circle is called a common tangent. The tangents can be classified into common tangents that are internal and external. An internal tangent is a line segment, which passes through the centre of the two circles whereas the external common tangents do not.

How many common tangents are there?

This lesson will talk about number of common tangents to two given circles….Lesson Summary.