MathDB
Maximalization + construction problem

Source: Kürschák 1989, problem 1

July 20, 2014
ratiogeometry unsolvedgeometry

Problem Statement

In the plane, two intersecting lines aa and bb are given, along with a circle ω\omega that has no common points with these lines. For any line ℓ∣∣b\ell||b, define A=ℓ∩aA=\ell\cap a, and {B,C}=ℓ∩ω\{B,C\}=\ell\cap \omega such that BB is on segment ACAC. Construct the line ℓ\ell such that the ratio ∣BC∣∣AB∣\frac{|BC|}{|AB|} is maximal.
Back to ProblemsView on AoPS