Cho tam giac ABC vuong tai A(AC>AB), duong cao AH trung tuyen AM.Cho BC=26cm, AH=12cm. C/m:
a) tinh HM va AB;
b) ve BN vuong goc AM tai N, BN cat AH tai I.C/m: BN=AH,
c) goi K la giao diem cua AB.C/m: M,I,K thang hang,
d) cho goc AMB=50 do tinh goc BIH va goc HIN,
e) c/m: IC { "@context": "https://schema.org", "@type": "QAPage", "mainEntity": { "@type": "Question", "name": " Cho tam giac ABC vuong tai A(AC>AB), duong cao AH trung tuyen AM.Cho BC=26cm, AH=12cm. C/m:
a) tinh HM va AB;
b) ve BN vuong goc AM tai N, BN cat AH t", "text": "Cho tam giac ABC vuong tai A(AC>AB), duong cao AH trung tuyen AM.Cho BC=26cm, AH=12cm. C/m: a) tinh HM va AB; b) ve BN vuong goc AM tai N, BN cat AH tai I.C/m: BN=AH, c) goi K la giao diem cua AB.C/m: M,I,K thang hang, d) cho goc AMB=50 do tinh goc BIH va goc HIN, e) c/m: IC
Đáp án:
e) Xét ΔHAM vuông tại có:
$\begin{array}{l}
\widehat {AMB} + \widehat {HAM} = {90^0}\\
\Leftrightarrow \widehat {HAM} = {40^0}\\
Do:\widehat {AMB} = \widehat {MAB}\\
\Leftrightarrow \widehat {MAB} = {50^0}\\
\Leftrightarrow \widehat {MAC} = {40^0}\\
\Leftrightarrow \widehat {IAC} = {80^0}\\
\Delta HIC:\widehat {IHC} = {90^0}\\
\widehat {AIC} > \widehat {IHC}\\
\Leftrightarrow \widehat {AIC} > {90^0}\\
\Leftrightarrow \widehat {AIC} > \widehat {IAC}\\
Trong:\Delta AIC:\widehat {AIC} > \widehat {IAC}\\
\Leftrightarrow AC > IC
\end{array}$
Vậy IC < AC