Question

The position vectors of $A,B,C,D$ are $\overline{a},\overline{b},\overline{c},\overline{d}$ respectively and $|\overline{a}-\overline{d}|=|\overline{b}-\overline{d}|=|\overline{c}-\overline{d}|$, then for the triangle $ABC$, $D$ is

• A. Ortho centre
• B. Centroid
• C. Circumcentre
• D. Incentre

Answer 1

The correct option is C Circumcentre

$|\overline{a}-\overline{d}|=|\overline{b}-\overline{d}|=|\overline{c}-\overline{d}|$

$\Rightarrow$ Point $D$ is equidistant from the points $A,B,C$ or the vertices of triangle.

$\Rightarrow D$ must be the circumcentre of the triangle.