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#### How Are Circles Used in Real Life? | Reference.com

https://www.reference.com/math/circles-used-real-life-5a9cee1968769425

Circles and their various properties, such as the radius, diameter, circumference and area, have applications in real life. If the radius of the circle is known, all the other parameters can be calculated. Important information can be determined for real life applications based on the parameters.

#### Circle Theorems - mathsisfun.com

https://www.mathsisfun.com/geometry/circle-theorems.html

Angle in a Semicircle (Thales' Theorem) An angle inscribed across a circle's diameter is always a right angle: (The end points are either end of a circle's diameter, the apex point can be anywhere on the circumference.)

#### Circle Theorems - Mathematics GCSE Revision

https://revisionmaths.com/gcse-maths-revision/shape-and-space/circle-theorems

The video below highlights the rules you need to remember to work out circle theorems. Isosceles Triangle. Two Radii and a chord make an isosceles triangle. Perpendicular Chord Bisection. The perpendicular from the centre of a circle to a chord will always bisect the chord (split it into two equal lengths). Angles Subtended on the Same Arc

#### Everything About Circle Theorems - In 3 minutes!

https://www.youtube.com/watch?v=XUus6-9E9sQ

This is a graphic, simple and memorable way to remember the difference from a chord or a tangent or a segments and sectors! I made this after struggling to understand it myself, once i got to ...

#### Three circle theorems in partial differential equations ...

https://scholarship.rice.edu/bitstream/handle/1911/89829/RICE0863.pdf?sequence=1

Three Circle Theorems in Partial Differential Equations and Applications to Improperly Posed Problems 1, Introductiono For complex valued functions analytic and single valued on an annulus, we know by Hadamard's three circle theorem  that the modulus on an intermediate circle must go

#### Descartes' theorem - Wikipedia

https://en.wikipedia.org/wiki/Descartes%27_theorem

In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation.By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.

#### Thales' Theorem | Geometry

http://www.mathspadilla.com/2ESO/Unit2-Geometry/thales_theorem.html

Two triangles are similar when they have equal angles and proportional sides.. THALES’ THEOREM: If we have three parallel straight lines, a, b and c, and they cut other two ones, r and r’, then they produce proportional segments :