MathDB

4

Part of 2014 Mexico National Olympiad

Problems(1)

Tangent line

Source: Mexico National Olympiad 2014

11/11/2014
Problem 4
Let ABCDABCD be a rectangle with diagonals ACAC and BDBD. Let EE be the intersection of the bisector of ∠CAD\angle CAD with segment CDCD, FF on CDCD such that EE is midpoint of DFDF, and GG on BCBC such that BG=ACBG = AC (with CC between BB and GG). Prove that the circumference through DD, FF and GG is tangent to BGBG.
geometryrectanglegeometric transformationreflectionnumber theorygeometry unsolvedtrigonometry