Question

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

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

Answer 1

The correct option is C

5 cm

In the $△$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 of the circle is 5 cm.