Question

if AB=12cm,BC=16cm and AB is perpendicular to BC,then find the radius of the circle passing through the points A,B and C......reply sooon plzz

Answer 1

Solution:-
Given : AB = 12 cm, BC = 16 cm and AB is ⊥ to BC
Now, applying Pythagoras Theorem,
Hypotenuse² = Perpendicular² + Base²
⇒ AC² = AB² + BC²
⇒ AC² = 12² + 16²
⇒ AC² = 144 + 256
⇒ AC² = 400 
⇒ AC = √400
AC = 20 cm
There is a relation between Hypotenuse (AC) and Circumradius (r).
The hypotenuse is the diameter of the circle and, and its center is exactly the midpoint of the hypotenuse.
So, Hypotenuse = 2r
Therefore,
r = hypotenuse/2
r = 20/2
Radius of the circle = 10 cm
Answer.