Apollonius Theorem is a popular part of elementary Geometry that is related to the length of the median of a triangle and length of its sides too. There are different names for the theorem is different regions and it can be proved by the Pythagorean Theorem by using cosine rule as well as vectors too. The theorem was named after the name of a Greek mathematician i. Apollonius of Perga.

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Apollonius Theorem is a popular part of elementary Geometry that is related to the length of the median of a triangle and length of its sides too. There are different names for the theorem is different regions and it can be proved by the Pythagorean Theorem by using cosine rule as well as vectors too. The theorem was named after the name of a Greek mathematician i.

Apollonius of Perga. Theorems are the popular statements in mathematics that had proven results based on previously set statements like axioms. The theorems are the proven results with accurate assumptions and a set of different axioms. When you will study mathematics during your school time or college periods, Theorems are an important part that is asked in the form of questions. Apollonius Theorem Proof Medians are the crucial set of components in geometry that are closely related to the Triangle and is independent of the geometric shapes too.

This is a popular theorem that connects the medians of a triangle with sides of a Triangle. Apollonius Theorem Generally understanding the proofs of Theorems are difficult. With the proper knowledge and educational background, you could derive the proof of a Theorem quickly. There is no quick way or shortcut method to construct the proof of the theorem. You should have a strong understanding of the concept and multiple logics to devise your proof. By continuous practice, you would be able to cultivate the proof the theorem by your own.

First, you should identify the problem what are you trying to prove and what is the final statement. You should also define the assumptions and questions that are necessary to work on before you start with the proof. When you are trying to understand the tough mathematical problems then worm on diagrams so that proof can be visualized clearly in front of your eyes.

Label each side and angle properly and get an idea of medians as well. You could refer books or online websites for the same to help you out. This is a common thing getting stuck on the proof and getting confused how can you devise the solution of a problem.

The best idea is to make a list of questions and try to solve them one by one to find the solution. This is always better to ask questions and experiment multiple time before you blindly cram the proof.

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## Problem of Apollonius

Circles sharing a radical axis[ edit ] Main article: Apollonian circles Figure 2. A set of Apollonian circles. Every blue circle intersects every red circle at a right angle, and vice versa. Every red circle passes through the two foci, which correspond to points A and B in Figure 1. The circles defined by the Apollonian pursuit problem for the same two points A and B, but with varying ratios of the two speeds, are disjoint from each other and form a continuous family that cover the entire plane; this family of circles is known as a hyperbolic pencil. Another family of circles, the circles that pass through both A and B, are also called a pencil, or more specifically an elliptic pencil. These two pencils of Apollonian circles intersect each other at right angles and form the basis of the bipolar coordinate system.

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## What is Apollonius Theorem? Apollonius Theorem Proof

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## Circles of Apollonius

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