MathDB
Shortlist 2017/G5

Source: IMO Shortlist 2017, Korea TST 2018

July 10, 2018
geometryperpendicular bisectorIMO Shortlist

Problem Statement

Let ABCC1B1A1ABCC_1B_1A_1 be a convex hexagon such that AB=BCAB=BC, and suppose that the line segments AA1,BB1AA_1, BB_1, and CC1CC_1 have the same perpendicular bisector. Let the diagonals AC1AC_1 and A1CA_1C meet at DD, and denote by ω\omega the circle ABCABC. Let ω\omega intersect the circle A1BC1A_1BC_1 again at E≠BE \neq B. Prove that the lines BB1BB_1 and DEDE intersect on ω\omega.
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