Question

 

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Answer 1

a) Xét \(\Delta MNP\) vuông tại M:

\(NP^2=MN^2+MP^2\left(Pytago\right).\\ \Rightarrow NP^2=5^2+12^2.\\ \Rightarrow NP^2=169.\\ \Rightarrow NP=13\left(cm\right).\)

b) Xét \(\Delta MNP\) vuông tại M:

MD là phân giác \(\widehat{NMP}\left(gt\right).\)

\(\Rightarrow\dfrac{ND}{DP}=\dfrac{MN}{MP}\) (T/c phân giác).

\(\Leftrightarrow\dfrac{ND}{ND+DP}=\dfrac{MN}{MP+MN}.\\ \Leftrightarrow\dfrac{ND}{NP}=\dfrac{MN}{MP+MN}.\\ \Rightarrow\dfrac{ND}{13}=\dfrac{5}{12+5}.\\ \Leftrightarrow\dfrac{ND}{13}=\dfrac{5}{17}.\\ \Rightarrow ND=\dfrac{65}{17}\left(cm\right).\\ \Rightarrow DP=NP-ND=13-\dfrac{65}{17}=\dfrac{156}{17}\left(cm\right).\)