MathDB
inequality for daigonal on isosceles trapezoid

Source: Sharygin Finals 2022 8.8

October 26, 2022
inequalitiesgeometrygeometric inequalityisoscelestrapezoid

Problem Statement

An isosceles trapezoid ABCDABCD (AB=CDAB = CD) is given. A point PP on its circumcircle is such that segments CPCP and ADAD meet at point QQ. Let LL be tha midpoint ofQD QD. Prove that the diagonal of the trapezoid is not greater than the sum of distances from the midpoints of the lateral sides to ana arbitrary point of line PLPL.