The figure below shows a triangle ABC
with the incenter I, a cevian BD, the circumcircle O and M midpoint of arc
AC. A line segment through I and perpendicular to the bisector of the
angle BDC intersects BD at E, and AC at F. MF extended intersects arc BC
at T. Prove that the circumcircle Q of the triangle EFT is tangent to BD
at E, AC at F, and arc BC at T.

See also: Typography and poster of problem 1408.

Geometry Problems

Ten problems: 1411-1420

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Triangle

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Circumcircle

Tangent Line

Tangent Circles

Angle Bisector

Perpendicular lines

Midpoint

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