MathDB
1/OK+ 1/OJ is contant for a line passing through a point on angle bisector

Source: 2004 Estonia National Olympiad Final Round grade 11 p2

March 25, 2020
Sumindependentfixedgeometryangle bisector

Problem Statement

Draw a line passing through a point MM on the angle bisector of the angle ∠AOB\angle AOB, that intersects OAOA and OBOB at points KK and LL respectively. Prove that the valus of the sum 1∣OK∣+1∣OL∣\frac{1}{|OK|}+\frac{1}{|OL|} does not depend on the choice of the straight line passing through MM, i.e. is defined by the size of the angle AOB and the selection of the point MM only.
Back to ProblemsView on AoPS