菱形ABCD点E、F在对角线BD上,BE=DF=1/4BD若四边形AECF为正方形求sin∠ABE

题目

菱形ABCD点E、F在对角线BD上,BE=DF=1/4BD若四边形AECF为正方形求sin∠ABE

答案

∵正方形AECF 设AE=a∴AE=AF=CE=CF AC、EF互相平分 ∠AEC=90°∴AC=√（AE²+CE²）=√2×a∵EF、AC互相平分∴AO=OC=√2/2×a∴OE=AO=√2/2×a∵BE=DF=1/4BD∴OB=2OE=√2×a∴AB=√（AO²+OB²）=√...