Giúp em câu 15 với ạ
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Đài ơi, giải giúp cho Sarah đi, tớ không có viết và giờ vào giường rồi , good nigh
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Câu 13:
ΔABC vuông tại A
=>\(AB^2+AC^2=BC^2\)
=>\(BC^2=6^2+8^2=100\)
=>\(BC=10\left(cm\right)\)
Xét ΔABC vuông tại A có AH là đường cao
nên \(AH\cdot BC=AB\cdot AC\)
=>\(AH\cdot10=6\cdot8=48\)
=>AH=48/10=4,8(cm)
Xét ΔABC vuông tại A có AH là đường cao
nên \(\left\{{}\begin{matrix}AB^2=BH\cdot BC\\AC^2=CH\cdot BC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}BH=\dfrac{6^2}{10}=3,6\left(cm\right)\\CH=\dfrac{8^2}{10}=6,4\left(cm\right)\end{matrix}\right.\)
Xét ΔHAB vuông tại H có HM là đường cao
nên \(BM\cdot BA=BH^2\)
=>\(BM\cdot6=3,6^2\)
=>BM=2,16(cm)
Xét ΔHAC vuông tại H có HN là đường cao
nên \(AN\cdot AC=AH^2\)
=>\(AN\cdot8=4,8^2\)
=>AN=2,88(cm)
ΔABN vuông tại A
=>\(AB^2+AN^2=BN^2\)
=>\(BN^2=2.88^2+6^2=44,2944\)
=>\(BN=\sqrt{44,2944}=\dfrac{6\sqrt{769}}{25}\left(cm\right)\)
Xét tứ giác AMHN có \(\widehat{AMH}=\widehat{ANH}=\widehat{MAN}=90^0\)
nên AMHN là hình chữ nhật
=>AH=MN=4,8(cm)
Xét ΔMBN có \(cosBMN=\dfrac{MB^2+MN^2-NB^2}{2\cdot MB\cdot MN}\)
\(=\dfrac{4,8^2+2,16^2-\dfrac{27684}{625}}{2\cdot4,8\cdot2,16}=\dfrac{-10368}{625}:\dfrac{2592}{125}=-\dfrac{4}{5}\)
=>\(sinBMN=\sqrt{1-\left(-\dfrac{4}{5}\right)^2}=\dfrac{3}{5}\)
Xét ΔBMN có \(\dfrac{NB}{sinBMN}=2R\)
=>\(2R=\dfrac{6\sqrt{769}}{25}:\dfrac{3}{5}=\dfrac{6\sqrt{769}}{25}\cdot\dfrac{5}{3}=\dfrac{2}{5}\sqrt{769}\)
=>\(R=\dfrac{\sqrt{769}}{5}\)
=>Chọn A
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cái giống như kiểu là già đình bn có hạnh phúc ko ý hả ?(đang ko hiểu mấy về cái đề)
Lời giải:
Gọi $O$ là giao điểm của $AC, BD$. Vì $AC\perp BD$ nên $AOB, AOD, DOC, BOC$ là tam giác vuông tại $O$.
Do đó, áp dụng định lý Pitago cho các tam giác trên thì:
$AD^2=AO^2+OD^2$
$BC^2=BO^2+OC^2$
$\Rightarrow AD^2+BC^2=OA^2+OB^2+OC^2+OD^2(1)$
$AB^2=AO^2+OB^2$
$CD^2=DO^2+CO^2$
$\Rightarrow AB^2+CD^2=OA^2+OB^2+OC^2+OD^2(2)$
Từ $(1);(2)\Rightarrow AD^2+BC^2=AB^2+CD^2$
Ta có đpcm.
Hình vẽ:
![](data:image/png;base64,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)