[PMO Tutorial #5] Stewart's Theorem - Geometry

Hello PMO Contestants!
Stewart's Theorem can be used to find the length of a cevian in a triangle. A cevian is a segment from a vertex to the opposite side. While not part of the high school curriculum, Stewart's Theorem can be proved using the Law of Cosines.
In this video, Issam Wang, former PMO National Finalist, solves two PMO problems using Stewart's Theorem.
Philippine Mathematical Olympiad
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Mathematical Society of the Philippines
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[@seanvillacampa5919]

das crazy dawg i love math sheesh shawty pareh

[@madscientist1595]

Thank you po sa knowledge, ganda po ng setup mas madali matandaan.
Stewart Theorem.
man + dad = bmb + cnc

[@dacurojezera.1280]

nice may mnemonic pa, tanong ko lang since theorem lang sya are there some cases of triangle na hindi sya pwede ma apply?

[@mathematicalsocietyoftheph8943]

It should apply to all triangles. If you look for a proof of this theorem, it doesn't assume what kind of triangle we have. Thus, whether the triangle is right, obtuse, acute, equilateral, isosceles, or scalene, Stewart's Theorem should apply.