a/ Xét \(ΔBNI\) và \(ΔBMA\):
\(\widehat{NBI}\) hay \(\widehat{MBA}\): chung
\(\widehat{BNI}=\widehat{BMA}(=90^\circ)\)
\(→ΔBNI\backsim ΔBMA(g-g)\)
\(\\ \)
b/ Xét \(ΔINB\) và \(ΔIMC\):
\(\widehat{INB}=\widehat{IMC}(=90^\circ)\)
\(\widehat{NIB}=\widehat{MIC}\) (đối đỉnh)
\(→ΔINB\backsim ΔIMC(g-g)\)
\(→\dfrac{IB}{IN}=\dfrac{IC}{IM}\)
\(→IB.IM=IC.IN\)
\(\\ \)
c/ Xét \(ΔCMI\) và \(ΔCNA\):
\(\widehat{CMI}=\widehat{CNA}(=90^\circ)\)
\(\widehat{ICM}\) hay \(\widehat{ACN}\): chung
\(→ΔCMI\backsim ΔCNA(g-g\)
\(→\dfrac{CM}{CI}=\dfrac{CN}{CA}\)
\(→CM.AC=CI.CN\)