MathDB

Let

ABC

be a triangle with midpoint

M

BC

. A point

X

is called immaculate if the perpendicular line from

X

to line

MX

intersects lines

AB

and

AC

at two points that are equidistant from

M

. Suppose

U, V, W

are three immaculate points on the circumcircle of triangle

ABC

. Prove that

M

is the incentre of

\triangle UVW

.
Proposed by Pranjal Srivastava and Rohan Goyal

Problem Statement