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题如图1,三段圆弧弧BC、弧CA、弧AB两两外切于A、B、C三点,圆I与弧BC、弧CA、弧AB分别外切于点D、E、F,点O是过A、B、C三点的圆的圆心.(1)求证:直线AD、BE、CF三线共点.(2)设直线AD、BE、CF三线共于点P,证明O、I、P三点共线.(注命题人对第一位解答正确者授予奖金50元.)有奖解题
The problem is shown in Figure 1. Three arcs of arc BC, arcs CA, and arcs AB are cut out at three points A, B, and C. Circles I and arcs BC, arcs CA, and arcs AB are cut at points D, E, respectively. F, point O is the circle center of A, B, C three points. (1) Verification: straight line AD, BE, CF three points common point. (2) Set straight line AD, BE, CF three lines are common to point P, prove O, I, P three points are collinear. (Note that the proposition person awards 50 yuan to the first correct person.) Prizes