MathDB
Geometric Maximization

Source: AIME 2008I Problem 14

March 23, 2008
trigonometryquadraticsgeometrygeometric transformationrotationAsymptotefunction

Problem Statement

Let AB‾ \overline{AB} be a diameter of circle ω \omega. Extend AB‾ \overline{AB} through A A to C C. Point T T lies on ω \omega so that line CT CT is tangent to ω \omega. Point P P is the foot of the perpendicular from A A to line CT CT. Suppose AB \equal{} 18, and let m m denote the maximum possible length of segment BP BP. Find m2 m^{2}.
Back to ProblemsView on AoPS