Question

Let $A(\alpha ,-2),B(\alpha ,6)$ and $C\left(\frac{\alpha }{4},-2\right)$ be vertices of a $△ABC$. If $\left(5,\frac{\alpha }{4}\right)$ is the circumcentre of $△ABC$, then which of the following is NOT correct about $△ABC$ :

• A. ares is 24
• B. perimeter is 25
• C. circumradius is 5
• D. inradius is 2

Answer 1

Answer: (B)

$A(\alpha ,-2):B(\alpha ,6):C\left(\frac{\alpha }{4},-2\right)$
since $AC$ is perpendicular to $AB$.
So, $△ABC$ is right angled at $A$.
Circumcentre$=\text{ mid point of }BC.=\left(\frac{5\alpha }{8},2\right)$
$\therefore \frac{5\alpha }{8}=5\&\frac{\alpha }{4}=2$
$\alpha =8$

$\text{ Area }=\frac{1}{2}(6)(8)=24$
Perimeter $=24$
Circumradius $=5$
Inradius $=\frac{\Delta }{s}=\frac{24}{12}=2$