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Triangle form by perpendicular bisector

Source: IMO Shortlist 2018 G5

July 17, 2019
geometry

Problem Statement

Let ABCABC be a triangle with circumcircle Ω\Omega and incentre II. A line ℓ\ell intersects the lines AIAI, BIBI, and CICI at points DD, EE, and FF, respectively, distinct from the points AA, BB, CC, and II. The perpendicular bisectors xx, yy, and zz of the segments ADAD, BEBE, and CFCF, respectively determine a triangle Θ\Theta. Show that the circumcircle of the triangle Θ\Theta is tangent to Ω\Omega.
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