MathDB
Locus of touch points between the ellipse and the line

Source: Sharygin Correspondence Round 2024 P22

March 6, 2024
conicsellipsegeometryperpendicular bisector

Problem Statement

A segment ABAB is given. Let CC be an arbitrary point of the perpendicular bisector to ABAB; OO be the point on the circumcircle of ABCABC opposite to CC; and an ellipse centred at OO touch AB,BC,CAAB, BC, CA. Find the locus of touching points of the ellipse with the line BCBC.