Question

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 correct option is C $10$ cm

It is given that $AB$ is perpendicular to $BC$, therefore, $\angle ABC={90}^{\circ }$.

Every angle inscribed in a semicircle is a right angle.

Since the inscribed $\angle ABC={90}^{\circ }$, the arc $ABC$ is a semicircle.

Therefore, $AC$ is the diameter of the circle passing through the centre.

Apply pythagorean theorem in triangle $ABC$, we have

${AC}^2={AB}^2{+BC}^2$

${AC}^2={12}^2{+16}^2$

${AC}^2=144+256$

${AC}^2=400$

$AC=\sqrt{400}$

$AC=20cm$

Diameter of circle is $20$ cm and hence the radius is $10$ cm as radius is half of diameter.