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设l是经过点A且平行于△ABC的边 BC的直线,D、E分别是 AC、AB上的点,连BD并延长交l于B_1,连CE并延长交 l于 C_l,BD、CE交于点 P.若 B_1D=C_lE,那么(1)当点P在△ABC的边BC的高上时,△ABC为等腰三角形;(2)当点P在∠BAC平分线上时,△ABC为等腰三角形.(注 第一位给出该命项直接证法者得奖全50元.奖由供题人设立)
Let l be a straight line passing through point A and parallel to △ABC’s edge BC, D, E are points on AC, AB respectively, connect BD and extend l to B_1, connect CE and extend l to C_l, BD, CE At intersection P. If B_1D=C_lE, then (1) When point P is on the high side BC of △ABC, △ABC is an isosceles triangle; (2) When point P is on the BAC bisector line, △ ABC is an isosceles triangle. (Note that the first person who gave the direct testimony of the item is awarded a full 50 yuan. The prize is set up by the donor.)