MathDB

16.

Part of 2024 Korea Junior Math Olympiad (First Round)

Problems(1)

Geometry

Source: 2024 KJMO first round

10/27/2024
There is an Equilateral trapezoid ABCD. ABCD. ABˉ=60,BCˉ=DAˉ=36,CDˉ=108. \bar{AB} =60, \bar{BC}=\bar{DA}= 36, \bar{CD}=108. M M is the middle point of ABˉ \bar {AB} , and point PP on AMˉ \bar{AM} follows that APˉ \bar {AP} =10. The foot of perpendicular dropped from PP to BDˉ \bar {BD} is EE. ACˉ∩BDˉ \bar{AC} \cap \bar{BD} is F F . Point XX is on AFˉ \bar {AF} which follows MXˉ=MEˉ \bar{MX}=\bar{ME} Find AXˉ×AFˉ \bar{AX} \times \bar{AF}
geometrytrapezoid