MathDB
Concurrency problem and calculation - [VMO 2011]

Source:

January 11, 2011
geometrytrigonometryprojective geometrygeometry proposed

Problem Statement

Let ABAB be a diameter of a circle (O)(O) and let PP be any point on the tangent drawn at BB to (O).(O). Define AP∩(O)=C≠A,AP\cap (O)=C\neq A, and let DD be the point diametrically opposite to C.C. If DPDP meets (O)(O) second time in E,E, then,
(i) Prove that AE,BC,POAE, BC, PO concur at M.M.
(ii) If RR is the radius of (O),(O), find PP such that the area of △AMB\triangle AMB is maximum, and calculate the area in terms of R.R.
Back to ProblemsView on AoPS