Given: The sides of the triangle are 4cm,7.5cm , and 8.5cm Concept used: Inradius: - The inradius of a triangle is formed by first dividing each of the three angles in half. - The point at which these three lines meet is the center of the incircle. - The inradius is a line drawn from the center to perpendicularly intersect a side of the triangle. - In-radius of a right angle triangle (r)=(P+B−H)∕2 Here, P= Perpendicular, B=Base,H= Hypotenuse Calculation:
Since 42+7.52=8.52 ⇒16+56.25=72.25 ⇒72.25=72.25‌ (Satisfying) ‌ Hence, the sides of the triangle are Pythagorean triplets According to the concept, In △ABC in-radius of the circle ⇒r=(AB+BC−AC)∕2 ⇒r=(4+7.5−8.5)∕2 ⇒r=3∕2=1.5 ∴ The radius of the circle inscribed is 1.5cm .