Difference between revisions of "2016 IMO Problems/Problem 1"
Alapan1729 (talk | contribs) (Created page with "Pr♦❜❧❡♠ ✶✳ ❚r✐❛♥❣❧❡ BCF ❤❛s ❛ r✐❣❤t ❛♥❣❧❡ ❛t B✳ ▲❡t A ❜❡ t❤❡ ♣♦✐♥t ♦♥ ❧✐♥❡ CF s✉❝❤...") |
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| − | + | Triangle BCF has a right angle at B.Let A be the point on line CF such that FA=FB and F lies between C and A. Point D is chosen such that DA=DC and AC is the bisector of ∠DAB. Point E is chosen such that EA=ED and AD is the bisector of ∠EAC. Let M be the midpoint of CF . Let X be the point such that AMXE is a parallelogram (where AM||EX and AE||MX). Prove that the lines BD,FX and ME are concurrent. | |
Revision as of 02:29, 8 June 2019
Triangle BCF has a right angle at B.Let A be the point on line CF such that FA=FB and F lies between C and A. Point D is chosen such that DA=DC and AC is the bisector of ∠DAB. Point E is chosen such that EA=ED and AD is the bisector of ∠EAC. Let M be the midpoint of CF . Let X be the point such that AMXE is a parallelogram (where AM||EX and AE||MX). Prove that the lines BD,FX and ME are concurrent.
