MathDB
2009 Geometry #4: Incircles and Kites

Source:

June 23, 2012
geometryratio

Problem Statement

A kite is a quadrilateral whose diagonals are perpendicular. Let kite ABCDABCD be such that ∠B=∠D=90∘\angle B = \angle D = 90^\circ. Let MM and NN be the points of tangency of the incircle of ABCDABCD to ABAB and BCBC respectively. Let ω\omega be the circle centered at CC and tangent to ABAB and ADAD. Construct another kite AB′C′D′AB^\prime C^\prime D^\prime that is similar to ABCDABCD and whose incircle is ω\omega. Let N′N^\prime be the point of tangency of B′C′B^\prime C^\prime to ω\omega. If MN′∥ACMN^\prime \parallel AC, then what is the ratio of AB:BCAB:BC?
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