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The figure shows a triangle ABC with the inscribed circle O (D, E, and T are the tangency points). OB cuts chord DE and arc DE at M and F, respectively. AF and CF cut chord DE at G and N, respectively. Prove that DG = MN.

See also: Art of problem 1312

#Geometry Problem 1315 #Triangle #Incircle #Tangent #Chord #Circle #Congruence #mathDetails: https://t.co/L6kJL5qKR7 pic.twitter.com/Cpzb9B1IjF— Antonio Gutierrez (@gogeometry) February 20, 2017

#Geometry Problem 1315 #Triangle #Incircle #Tangent #Chord #Circle #Congruence #mathDetails: https://t.co/L6kJL5qKR7 pic.twitter.com/Cpzb9B1IjF

Hey @gogeometry :This @geogebra one's 4u-(Great problem!) https://t.co/hIPmZDDdyH #MTBoS #geometry #HSMath #CollegeMath #math #mathchat pic.twitter.com/d4BHkdGTuS— Tim Brzezinski (@dynamic_math) February 20, 2017

Hey @gogeometry :This @geogebra one's 4u-(Great problem!) https://t.co/hIPmZDDdyH #MTBoS #geometry #HSMath #CollegeMath #math #mathchat pic.twitter.com/d4BHkdGTuS

#Math Enthusiasts: Why does THIS phenomenon (at the end) hold true? Credit: @gogeometry https://t.co/hIPmZDDdyH @geogebra #mathchat #mathGIF pic.twitter.com/wGfy23hDyx— Tim Brzezinski (@dynamic_math) August 21, 2017

#Math Enthusiasts: Why does THIS phenomenon (at the end) hold true? Credit: @gogeometry https://t.co/hIPmZDDdyH @geogebra #mathchat #mathGIF pic.twitter.com/wGfy23hDyx

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