How to know if a quadrilateral is circumscribed

Question

Let's say I have a quadrilateral that is convex and I know the points that are forming it. How can I know if the quadrilateral is circumscribed? Is it true that a quadrilateral is circumscribed if and only if the sum of opposite sides are equal?

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In my case, picture above, only if $AB+CD=AC+BD$?

I should be called tangential quadrilateral. See the classification here. — Ng Chung Tak, Dec 07 '16 at 14:15

score 0 · Accepted Answer · answered Dec 07 '16 at 14:13

0

It's true. It's Pitot's Theorem and its converse.

See http://www.cut-the-knot.org/Curriculum/Geometry/Pitot.shtml

answered Dec 07 '16 at 14:13

Ethan Bolker

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How to know if a quadrilateral is circumscribed

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