$$\eqalign{
& \overrightarrow {{n_{AB}}} = \left( {1; - 7} \right);\,\,\overrightarrow {{n_{BC}}} = \left( {2;1} \right) \cr
& \Rightarrow \cos \widehat {ABC} = {{\left| {\overrightarrow {{n_{AB}}} .\overrightarrow {{n_{BC}}} } \right|} \over {\left| {\overrightarrow {{n_{AB}}} } \right|.\left| {\overrightarrow {{n_{BC}}} } \right|}} = {{\left| {1.2 - 7.1} \right|} \over {\sqrt {50} \sqrt 5 }} = {1 \over {\sqrt {10} }} \cr
& Goi\,\,c\left( {c;2 - 2c} \right) \in BC \cr
& \overrightarrow {MC} = \left( {c; - 2c - 2} \right);\,\,\overrightarrow {{u_{BC}}} = \left( {1; - 2} \right) \cr
& \cos \widehat {ACB} = {{\left| {c + 4c + 4} \right|} \over {\sqrt {{c^2} + {{\left( {2c + 2} \right)}^2}} \sqrt 5 }} = {{\left| {5c + 4} \right|} \over {\sqrt {{c^2} + {{\left( {2c + 2} \right)}^2}} \sqrt 5 }} = {1 \over {\sqrt {10} }} \cr
& \Leftrightarrow 2{\left( {5c + 4} \right)^2} = {c^2} + {\left( {2c + 2} \right)^2} \cr
& \Leftrightarrow 50{c^2} + 80c + 32 = {c^2} + 4{c^2} + 8c + 4 \cr
& \Leftrightarrow 45{c^2} + 72c + 28 = 0 \cr
& \Leftrightarrow \left[ \matrix{
c = - {2 \over 3} \Rightarrow C\left( { - {2 \over 3};{{10} \over 3}} \right) \hfill \cr
c = - {{14} \over {15}} \Rightarrow C\left( { - {{14} \over {15}};{{58} \over {15}}} \right) \hfill \cr} \right. \cr
& Thu\,\,lai:\,\,C\left( { - {{14} \over {15}};{{58} \over {15}}} \right) \Rightarrow \overrightarrow {CM} = \left( {{{14} \over {15}};{2 \over {15}}} \right)//\left( {7;1} \right) \cr
& \Rightarrow CM//AB\,\,\left( {loai} \right) \cr
& Vay\,\,C\left( { - {2 \over 3};{{10} \over 3}} \right) \cr} $$
