Question

If $AB=12\text{cm},BC=16\text{cm}$, and $AB$ is perpendicular to $BC$, then the radius of the circle passing through the points $A,B,$ and $C$ is:

• A. $10\text{cm}$
• B. $8\text{cm}$
• C. $20\text{cm}$
• D. $6\text{cm}$

Answer 1

The correct option is A $10\text{cm}$

$AB=12\text{cm},BC=16\text{cm}$
$AC$ is a hypotenuse of triangle $ABC$
And $AC$ is the diameter of the circle
Now $AC=\sqrt{{AB}^2+{BC}^2}$
$AC=\sqrt{{12}^2+{16}^2}$
$AC=\sqrt{144+256}$
$AC=400=20\text{cm}$
So Radius of circle $=\frac{\text{Diameter}}{2}=\frac{20}{2}=10\text{cm}$