What are Symmedians? How are they used?

In this video, I introduce symmedians and three characterisations: Angle, locus and length based criteria. We also identify a common configuration in which symmedians arise.
00:15 What is a 'symmedian'?
01:06 Angle condition for symmedian (useful for angle chasing)
01:33 What is an 'antiparallel' to a side in a triangle? How antiparallels produce cyclic quadrilaterals?
03:00 The locus of the midpoints of A-antiparallels is the A-symmedian.
04:45 The ratio of lengths critieria for points on a symmedian. (derivation)
07:22 The ratio of lengths critieria for points on a symmedian. (statement)
07:45 The pair of tangents configuaration and the symmedian
11:45 Solution to a March Crux problem using Symmedians featured on my blog.
11:54 A short proof of Polish 2000 Math Olympiad problem using Symmedians.
Link to the article on my website: mudhitha.com/crux-4921-using-...
Link to Ray Li's handout on Symmedians: cs.stanford.edu/~rayyli/stati...

[@OreoCheesecakee272]

Very nice video. Bring more such topics

[@MudithaMath]

Thanks for the comment. I was not sure if people are interested in specialized configurations. You have encouraged me to do a few more videos like this :)

[@mathsinmo4372]

very nice video can you bring a series for inmo 2025