(1)如图1,分别以AC,CB为边向形外作正方形ACDE和正方形BGFC.记正方形ACDE的面积为,正方形BGFC的面积为.
①若,,求S的值;
②延长EA交GB的延长线于点N,连结FN,交BC于点M,交AB于点H.若FH⊥AB(如图2所示),求证:.
(2)如图3,分别以AC,CB为边向形外作等边三角形ACD和等边三角形CBE,记等边三角形ACD的面积为,等边三角形CBE的面积为.以AB为边向上作等边三角形ABF(点C在△ABF内),连结EF,CF.若EF⊥CF,试探索与S之间的等量关系,并说明理由.
同类型试题
y = sin x, x∈R, y∈[–1,1],周期为2π,函数图像以 x = (π/2) + kπ 为对称轴
y = arcsin x, x∈[–1,1], y∈[–π/2,π/2]
sin x = 0 ←→ arcsin x = 0
sin x = 1/2 ←→ arcsin x = π/6
sin x = √2/2 ←→ arcsin x = π/4
sin x = 1 ←→ arcsin x = π/2
y = sin x, x∈R, y∈[–1,1],周期为2π,函数图像以 x = (π/2) + kπ 为对称轴
y = arcsin x, x∈[–1,1], y∈[–π/2,π/2]
sin x = 0 ←→ arcsin x = 0
sin x = 1/2 ←→ arcsin x = π/6
sin x = √2/2 ←→ arcsin x = π/4
sin x = 1 ←→ arcsin x = π/2