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circumcenter is equidistant from B,C (HOMC 2018 S Team 9)

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February 17, 2020
geometryperpendicularCircumcentersimilar triangles

Problem Statement

Let ABCABC be acute, non-isosceles triangle, inscribed in the circle (O)(O). Let DD be perpendicular projection of AA onto BCBC, and E,FE, F be perpendicular projections of DD onto CA,ABCA,AB respectively. (a) Prove that AO⊥EFAO \perp EF. (b) The line AOAO intersects DE,DFDE,DF at I,JI,J respectively. Prove that △DIJ\vartriangle DIJ and △ABC\vartriangle ABC are similar. (c) Prove that circumcenter of △DIJ\vartriangle DIJ is equidistant from BB and CC
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