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 .