Question

The line segments $AB$ and $BC$ are perpendicular to each other. If $AB=4$ cm and $BC=3$ cm, then radius of the circle passing through A, B, C will be

• A. $3.5$ cm
• B. $2.0$ cm
• C. $2.5$ cm
• D. $4.5$ cm

Answer 1

The correct option is C $2.5$ cm

As we know that angle formed in a semi circle is always a right angle as shown in figure according to the question.

So, in $△ABC$,

$A{C}^2=A{B}^2+B{C}^2$

$A{C}^2=4^2+3^2$

$A{C}^2=25$

$AC=5$ cm

As $AC$ is the diameter hence, the radius will be $2.5cm$.

This is the required solution.