Question

If the lengths of sides of triangle are $6cm,8cm$, and $10cm$, then let us write where the circumcentre of this triangle lies.

Answer 1

Given: lengths of sides of triangle are $6cm,8cm$, and $10cm$.
Let $AC=10cm,BC=8cm$ and $AB=6cm$
To be a right angle triangle,
$(AC{)}^2=(AB{)}^2+(BC{)}^2$
$(10{)}^2=(8{)}^2+(6{)}^2$
$100=64+36$
$100=100$
Hence, LHS = RHS
So, it is a right angle triangle.
In a right angle triangle circumcentre lies on hypotenuse.