在Rt△ABC中,AC=BC,∠ACB=90°,D為BC上一點(diǎn).
(1)如圖1,過C作CE⊥AB于E,連接AD,DE.若AD平分∠BAC,CD=3,求DE的長(zhǎng);
(2)如圖2,以CD為直角邊,點(diǎn)C為直角頂點(diǎn),向右作等腰直角三角形△DCM,將△DCM繞點(diǎn)C順時(shí)針旋轉(zhuǎn)α°(0<α<45),連接AM,BD,取線段AM的中點(diǎn)N,連接CN.求證:BD=2CN;
(3)如圖3,連接AD,將△ACD沿AD翻折至△ADF處,在BC上取點(diǎn)H,連接AH,過點(diǎn)F作FQ⊥AH交AC于點(diǎn)Q,F(xiàn)Q交AH于點(diǎn)G,連接CG,若FQ:AH=
:2,AB=4,當(dāng)CG取得最小值時(shí),求△ACG的面積.