Welcome to 9math!

This site is for those who are interested in mathematics, whether they want to study it for school or as a hobby.

If you have math questions you can ask them on the forum.

On this site you can write nice mathematical expressions and equations by using Latex and the visual Equation Editor:


You can use the mouse to play with the interactive geometry figures.

You can also draw functions' graphs fast:

If you wish to learn new notions and tricks you can read the documentation (Algebra, Analysis, Arithmetic, Geometry) that we are developing.

Look at the recent posts to keep up with the latest activity.

Also read the FAQ and Help for more information.

Circle of nine points

IMO 2013 geometry problem 4

Let ABC be an acute triangle with orthocenter H, and let W be a point on the side BC, between B and C. The points M and N are the feet of the altitudes drawn from B and C, respectively. $ \omega_1 $ is the circumcircle of triangle BWN, and X is a point such that WX is a diameter of $ \omega_1 $. Similarly, $ \omega_2 $ is the circumcircle of triangle CWM, and Y is a point such that WY is a diameter of $  \omega_2 $. Show that the points X, Y, and H are collinear.
(point A 151 84)
(point B 92 260)
(point C 310 258)
(segment d1 A B)
(line d2 B C)
(segment d3 C A)
(projection N C d1)

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