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# Inversion and Ptolemy’s Theorem

Ptolemy’s theorem can be proved by inversion. Learn it using this beautifully crafted video (involving animated mathematics). It also includes problems.

# Understand the problem

Ptolemy’s Theorem gives a relation between product of diagonals of a quadrilateral with the sum of the product of its opposite sides. However it can be proved using tools from inversive geometry (that Ptolemy probably did not know). Try this!

# Now watch the discussion video #### Kazi Abu Rousan

Cheenta Creative Team

Kazi is a student of Physics. He loves the relation between physics and mathematics. He is the creator of this beautiful video.

# Tutorial Problems… try these after watching the video.

1. How can you generalize Ptolemy’s theorem if the quadrilateral is not cyclic?? 2. Suppose two points A, B, are inside a unit circle G. Invert A and B about G to A’ and B’ respectively. If the length of AB is 0.5, what is the length of A’B’? You may send solutions to support@cheenta.com. Though we usually look into internal students’ work, we will try to give you some feedback.

# Connected Program at Cheenta

Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.

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## One reply on “Inversion and Ptolemy’s Theorem”

Impressive Demonstration!

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