Question

Fill In The Blanks

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 _________.

Answer 1

Given:
AB = 12 cm
BC = 16 cm
AB is perpendicular to BC


Since, AB is perpendicular to BC
Therefore, the circle formed by joining A, B and C is a circle with diameter AC.

In ∆ABC,
Using pythagoras theorem,
AB² + BC² = AC²
⇒ 12² + 16² = AC² (given)
⇒ 144 + 256 = AC²
⇒ AC²= 400
⇒ AC = 20

Thus, the diameter of the circle is 20 cm.
Therefore, the radius of the circle is half of the diameter of the circle.
Radius = $\frac{1}{2}\left(20\right)$ =10 cm

Hence, the radius of the circle passing through the points A, B and C is 10 cm.