Đáp án:
\(\left| {\overrightarrow {DA} + \overrightarrow {DC} } \right| = a\sqrt 2 \)
Giải thích các bước giải:
\(\eqalign{
& \overrightarrow {BD} - \overrightarrow {BC} = \overrightarrow {CD} \cr
& \overrightarrow {CO} - \overrightarrow {OB} = \overrightarrow {CO} + \overrightarrow {BO} = 2\overrightarrow {IO} \,\,\left( {I\,\,la\,\,TD\,\,cua\,\,BC} \right) \cr
& IO\,\,la\,\,duong\,\,TB\,\,cua\,\,\Delta BCD. \cr
& \Rightarrow CD = 2IO \Rightarrow \overrightarrow {CD} = 2\overrightarrow {IO} \cr
& \Rightarrow \overrightarrow {BD} - \overrightarrow {BC} = \overrightarrow {CO} - \overrightarrow {OB} \cr
& \left| {\overrightarrow {DA} + \overrightarrow {DC} } \right| = \left| {2\overrightarrow {DO} } \right| = 2DO = BD \cr
& Ap\,\,dung\,\,dinh\,\,li\,\,Pytago\,\,trong\,\,\Delta ABD: \cr
& B{D^2} = A{B^2} + A{D^2} = {a^2} + {a^2} = 2{a^2} \cr
& \Rightarrow BD = a\sqrt 2 \cr
& \Rightarrow \left| {\overrightarrow {DA} + \overrightarrow {DC} } \right| = a\sqrt 2 \cr} \)
