Question

If $\overline{a},\overline{b},\overline{c},\overline{d}$ are the position vectors of four points $A,B,C,D$ in a plane such that $|\overline{a}-\overline{d}|=|\overline{b}-\overline{d}|=|\overline{c}-\overline{d}|$ then the point $D$ is the$\cdots$ of $\Delta ABC$

• A. centroid
• B. circumcentre
• C. orthocentre
• D. incentre

Answer 1

The correct option is B circumcentre

$\left|\overrightarrow{DA}\right|=\left|\overrightarrow{DB}\right|=\left|\overrightarrow{DC}\right|$
D is circumcentre
where $\left|\overrightarrow{DA}\right|=\left|\overrightarrow{DB}\right|=\left|\overrightarrow{DC}\right|=R$