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原问题[1]设圆内接四边形ABCD的两组对边延长后分别交于点E、F,对角线AC和BD的中点分别为M和N.求证:MN/EF=1/2︱AC/BD-BD/AC︱.拓展问题设四边形ABCD的两组对边延长后分别交于点E、F,对角线AC和BD的中点分别为M和N.求证:直线MN平分EF.证明如图所示.设T为EF的中点,过点M作BE的平行线分别交BC、EC于点R、Q,则R、Q分别为BC、EC的中点,又设P为BE的中点,则点P、R、N
The original problem [1] set the circle within the quadrilateral ABCD two pairs of extension of the line after the intersection of points E, F, diagonal AC and BD of the midpoints were M and N. Verify: MN / EF = 1/2 ︱ AC / BD-BD / AC | .Expansion problem Let quadrilateral ABCD set of two pairs of side extension after the intersection of points E, F, diagonal AC and BD of the midpoints were M and N. Verify: straight line MN bisect EF. As shown in the figure, let T be the midpoint of EF and let M be the parallel line of BE for BC and EC, respectively. For R and Q, R and Q are the midpoints of BC and EC respectively. P is the midpoint of BE, the point P, R, N