MathDB

1

Part of 1989 Kurschak Competition

Problems(1)

Maximalization + construction problem

Source: Kürschák 1989, problem 1

7/20/2014
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.
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