Question

Question 3
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

(A) 6 cm
(B) 8 cm
(C) 10 cm
(D) 12 cm

Answer 1

The answer is C.

Given, AB = 12 cm and BC = 16 cm
In the circle, BC $\perp$ AB, it means that AC will be a diameter of circle.
[diameter of a circle subtends a right angle to the circle]
Use Pythagoras theorem in right angled $\Delta ABC$.
$\begin{array}{cc}& A{C}^2=A{B}^2+B{C}^2\\ \Rightarrow & A{C}^2=(12{)}^2+(16{)}^2\\ \Rightarrow & A{C}^2=144+256\Rightarrow A{C}^2=400\\ \Rightarrow & AC=\sqrt{400}=20cm\end{array}$
[taking positive square root, because diameter is always positive]
$\therefore$ Radius of circle $=\frac{1}{2}\left(AC\right)=\frac{1}{2}\times 20=10cm$
Hence the radius of circle is 10 cm.