MathDB
Problem 1(Geometry)

Source: SRMC 2002

September 16, 2007
geometrycircumcircleangle bisectorgeometry proposed

Problem Statement

Let △ABC \triangle ABC be a triangle with incircle ω(I,r) \omega(I,r)and circumcircle ζ(O,R) \zeta(O,R).Let la l_{a} be the angle bisector of ∠BAC \angle BAC.Denote P\equal{}l_{a}\cap\zeta.Let D D be the point of tangency ω \omega with [BC] [BC].Denote Q\equal{}PD\cap\zeta.Show that PI\equal{}QI if PD\equal{}r.
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