Question

Triangle $ABC$ has $AB=5,$ $BC=12$ and $AC=13.$ The perpendicular bisector of $AC$ intersects the extension of $AB$ at $O.$ Then $OC$ is

• A. $\frac{169}{5}$
• B. $\frac{169}{10}$
• C. $\frac{5}{2}$
• D. $\frac{2}{5}$

Answer 1

The correct option is B $\frac{169}{10}$


Let $M$ be the mid-point of $AC.$
$△OAM\cong OCM$
$\therefore OA=OC$

Also, $△ABC\sim △AMO$
$\Rightarrow \frac{AB}{AC}=\frac{AM}{AO}$
$\Rightarrow OA=OC=AM\cdot \frac{AC}{AB}$
$\Rightarrow OA=\frac{13}{2}\cdot \frac{13}{5}=\frac{169}{10}$