If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is:
Given: AB = 12 cm, BC = 16 cm, AB ⊥ BC.
Therefore, the circle passing through the points A, B and C has AC as its diameter.
So, from the figure, ABC is a right angled trianlge.
By Pythagoras theorem:
(AC)2 = (CB)2 + (AB)2
⇒ (AC)2 = (16)2 + (12)2
⇒ (AC)2 = 256 + 144
⇒ (AC)2 = 400
Take square root on both sides:
⇒ (AC) = 20
∴ Diameter of the circle = 20 cm
Thus, radius of the circle = Diameter/2 = 20/2 = 10 cm
∴ Radius of the circle = 10 cm
4