Question

In the given figure, AB $=5cm,$ BC $=4cm,$ AC $=3cm.$ What is the diameter of the circle?

​

• A. 3 cm
• B. 2.5 cm
• C. 5 cm
• D. 4 cm

Answer 1

The correct option is C

5 cm

In $△$ABC, $A{B}^2=A{C}^2+B{C}^2$
Thus, AC and BC forms the perpendicular sides of the $△$ABC
Thus, $\angle C={90}^{\circ }$
We know by theorem that angle subtended by diameter at any point on circle is ${90}^{\circ }$.

So, using the property we come to know that the line segment AB is the diameter of the circle. Also, the length of the AB is given; therefore, the diameter length of the circle is $5cm.$