For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals.

We have three colored segment in this animation. Surprisingly the length of the longest one is always the sum of the length of the two smaller ones.

This is actually a very special case of Ptolemy’s theorem. The theorem gives a connection between the sides and the diagonals of a cyclic quadrilateral. In this case the length of the dashed lines is equal so the theorem can be simplified to the statement above.

Get informed:

http://mathworld.wolfram.com/PtolemysTheorem.html

Source:

http://szimmetria-airtemmizs.tumblr.com/

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January 21, 2019 at 6:58 am

Love your blog!

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January 21, 2019 at 6:58 am

Merci 🙂

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January 22, 2019 at 4:12 pm

This is only very slightly related but is the weirdest math thing I have seen in years: https://www.youtube.com/watch?v=HEfHFsfGXjs insofar as the conclusion is just so totally unexpected.

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