@nan
a)
$\text{ta có }$
$\text{A : B : C : D = 5 :8 :13 :10}$
$\text{$\widehat{A}$}$ = $\frac{1}{2 }$ $\widehat{D}$
$\text{$\widehat{B}$}$ = $\frac{4}{5}$ $\widehat{D}$
$\text{$\widehat{C}$}$ = $\frac{13}{10}$ $\widehat{D}$
$\text{Vậy A + B + C + D = }$$360^{0}$
$\text{Suy ra }$
$\text{$\widehat{A}$}$ = $\frac{1}{2 }$ $\widehat{D}$
$\text{$\widehat{B}$}$ = $\frac{4}{5}$ $\widehat{D}$
$\text{$\widehat{C}$}$ = $\frac{13}{10}$ $\widehat{D}$
$\text{ A + B + C + D = }$$360^{0}$
⇒ $\text{A = }$$56^{0}$
$\text{B =}$$80^{0}$
$\text{C = }$$130^{0}$
$\text{D = }$$100^{0}$
___________________________________
B)
$\text{$\Delta$ABF+ $\Delta$AFB = }$$180^{0}$ - A - B = $50^{0}$
$\text{SUY RA AFM = }$$25^{0}$
$\text{NME = DMF = }$$180^{0}$ - ( $180^{0}$ - D ) - $25^{0}$ = $75^{0}$
⇒ $\text{AED = }$$30^{0}$
⇒ $\text{MNE = MNE = }$$75^{0}$
$\text{Vậy O là trung trực của MN }$
