Đáp án: $MN=\dfrac{75}{4}$
Giải thích các bước giải:
Ta có $AB//CD$
$\to \dfrac{OA}{OC}=\dfrac{OB}{OD}=\dfrac{AB}{CD}=\dfrac35$
$\to \dfrac{OA}{OA+OC}=\dfrac{OB}{OB+OD}=\dfrac3{3+5}$
$\to \dfrac{OA}{AC}=\dfrac{OB}{BD}=\dfrac38$
Ta có $MN//AB//CD$
$\to \dfrac{OM}{CD}=\dfrac{AO}{AC}=\dfrac{BO}{BD}=\dfrac{ON}{CD}$
$\to OM=ON$
$\to MN=2OM$
Mặt khác $\dfrac{OM}{CD}=\dfrac{AO}{AC}=\dfrac38$
$\to OM=\dfrac38CD=\dfrac{75}{8}$
$\to MN=2OM=\dfrac{75}{4}$