Given,
A(\alpha ,-2),B(\alpha ,6)&C(\frac{\alpha }{4},-2)
Now slope of AC=0 and slope of AB=08→∞
Now we can see AC is perpendicular to AB.
So, ΔABC is right angled at A.
So, Circumcentre =mid point of BC=(85α,2)
Now given circumcentre ≡(5,4α)
So on comparing we get,\frac{5\alpha }{8}=5&\frac{\alpha }{4}=2
⇒α=8
Now plotting the diagram and finding the sides with distance formula we get,

Area =21(6)(8)=24
Perimeter =24
Circumradius =210=5
Inradius =sΔ=1224=2