MathDB

P22

Part of 2017 Sharygin Geometry Olympiad

Problems(1)

distance from a point on diagonal of a cyclic quadrilateral

Source: Sharygin Geometry Olympiad 2017 First Round P22 grades 10-11

7/23/2018
Let PP be an arbitrary point on the diagonal ACAC of cyclic quadrilateral ABCDABCD, and PK,PL,PM,PN,POPK, PL, PM, PN, PO be the perpendiculars from PP to AB,BC,CD,DA,BDAB, BC, CD, DA, BD respectively. Prove that the distance from PP to KNKN is equal to the distance from OO to MLML.
geometrycyclic quadrilateraldistanceprojection