Giải thích các bước giải:
a.Ta có $AB//CD$
$\to \dfrac{AO}{AC}=\dfrac{BO}{BD}$
Lại có: $OE//CD, OF//CD\to \dfrac{OE}{DC}=\dfrac{AO}{AC}=\dfrac{BO}{BD}=\dfrac{OF}{CD}$
$\to OE=OF$
b.Ta có:
$\dfrac{OE}{CD}=\dfrac{AO}{AC}$
Lại có:
$OE//AB\to \dfrac{OE}{AB}=\dfrac{DO}{DB}=\dfrac{CO}{CA}$
$\to \dfrac{OE}{CD}+\dfrac{OE}{AB}=\dfrac{AO}{AC}+\dfrac{CO}{AC}=1$
$\to OE(\dfrac{1}{CD}+\dfrac{1}{AB})=1$
$\to OE\cdot \dfrac{AB+CD}{AB\cdot CD}=1$
$\to OE=\dfrac{AB\cdot CD}{AB+CD}$
$\to OF=OE=\dfrac{AB\cdot CD}{AB+CD}$