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(2013?绵阳)如图,四边形ABCD是菱形,对角线AC=8cm,BD=6cm,DH⊥AB于点H,且DH与AC交于G,则GH=(
(2013?绵阳)如图,四边形ABCD是菱形,对角线AC=8cm,BD=6cm,DH⊥AB于点H,且DH与AC交于G,则GH=()A.2825cmB.2120cmC.28...
(2013?绵阳)如图,四边形ABCD是菱形,对角线AC=8cm,BD=6cm,DH⊥AB于点H,且DH与AC交于G,则GH=( )A.2825cmB.2120cmC.2815cmD.2521cm
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∵四边形ABCD是菱形,对角线AC=8cm,BD=6cm,
∴AO=4cm,BO=3cm,
在Rt△AOB中,AB=
=5cm,
∵
BD×AC=AB×DH,
∴DH=
cm,
在Rt△DHB中,BH=
=
cm,
则AH=AB-BH=
cm,
∵tan∠HAG=
=
=
,
∴GH=
AH=
cm.
故选B.
∴AO=4cm,BO=3cm,
在Rt△AOB中,AB=
AO2+BO2 |
∵
1 |
2 |
∴DH=
24 |
5 |
在Rt△DHB中,BH=
DB2?DH2 |
18 |
5 |
则AH=AB-BH=
7 |
5 |
∵tan∠HAG=
GH |
AH |
OB |
AO |
3 |
4 |
∴GH=
3 |
4 |
21 |
20 |
故选B.
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