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1 题 设以ｒ为半径的圆内接正 2 0 0 2边形Ａ1Ａ2 …Ａ2 0 0 2 ,在圆内取与圆心距离为ａ的一点Ｐ。试证 :ＰＡ21+ＰＡ22 +… +ＰＡ22 0 0 2 =2 0 0 2 (ｒ2 +ａ2 )。证明 设∠ＰＯＡ1=θ,则∠ＰＯＡ2 =θ + 2π2 0 0 2 , ∠ＰＯＡ3 =θ + 2× 2π2 0 0 2 ,…… ,∠ＰＯＡ2 0
1 Question Let R be the radius of the circle in the positive 2 0 0 2 edge A1A2 ... A2 0 0 2 , take a point P in the circle with a center distance a. Testimony: PA21+PA22 +... +PA22 0 0 2 =2 0 0 2 (r2 +a2 ). Proof Let ∠ POA1 = θ, then ∠ POA2 = θ + 2π2 0 0 2 , ∠POA3 = θ + 2× 2π2 0 0 2 ,..., ∠ POA2 0