Problem 767: Equilateral Triangle, Circle tangent to a
side, Tangent line, Measurement, Secant. Level: High School, College,
The figure shows an equilateral triangle ABC with
AC tangent to a circle O at T. Circle O cuts AB and BC at D,E,F,G,
respectively. Prove that: AT + BD + BE = CT + BF + BG. This entry contributed by Ajit Athle.