MathDB
Geometry with beautiful analytic solution

Source:

December 17, 2019
geometry

Problem Statement

Let be a point P P on the diagonal BD BD (excluding its endpoints) of a quadrilateral ABCD, ABCD, and Q Q be a point in the interior of ABD. ABD. The projections of P P on AB,AD AB,AD are P1,P2, P_1,P_2, respectively, and the projections of Q Q on AB,AD AB,AD are Q1,Q2, Q_1,Q_2, respectively, and verify the equations AQ1=14AB AQ_1=\frac{1}{4}AB and AQ2=14AD. AQ_2=\frac{1}{4}AD. Show that the point Q Q is not in the interior of AP1P2. AP_1P_2.
Back to ProblemsView on AoPS