MathDB

1

Part of 2002 Silk Road

Problems(1)

Problem 1(Geometry)

Source: SRMC 2002

9/16/2007
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.
geometrycircumcircleangle bisectorgeometry proposed