Show that the line joining the mid-points of the diagonals of a trapezoid is half the difference of its bases.
Show that the line joining the mid-points of the diagonals of a trapezoid is half the difference of its bases.
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于圆内接四边形内,若两对角线成垂直,求证对角线交点与一边中点之距离等于自圆心至对边之距离.
证明:对于一组共轴圆 (co-axial circles) 一定点之诸极线 (polars) 必通过一定点,且一定直线之诸极 (poles) 必在一直线上.
以 n 角形之顶点为顶点,而不是 n 角形之边为边之三角形共有若干?
某城街路为棋盘式,走向南北者有 a 条,而走向东西者有 6 条,一行人欲由西北隅向最短之路走到东南隅,问计共有若干方法?
圆之直径 AB 上任意取 P 点,又 CD 与直径平行,求证 AP² + BP²=CP² + DP².
设 ABC 为一直角三角形,A 为直角,A 之平分线与 BC 交于 D,与此三角形之外接圆交于 B.求证: △ABC 之面积 =1/2 AD×AE.
已知直线 y = kx + b (k > 0) 与圆 x2 + y2 = 1 和圆 (x − 4)2 + y2 = 1 均相切, 则 k = _______, b = _______.