Question

In the given figure, AB = 5cm, BC = 4cm, AC = 3cm. Find the length of 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 the $△$ABC, $A{C}^2+B{C}^2=3^2+4^2$

$A{C}^2+B{C}^2=9+16$

$A{C}^2+B{C}^2=25$
$A{C}^2+B{C}^2=A{B}^2$

By Converse of Pythagoras Theorem, $△$ABC is right angled at C.

Thus, $\angle C={90}^{\circ }$
We know that angle subtended by diameter at any point on circle is ${90}^{\circ }$.

So, using this property we can conclude that the line segment AB is the diameter of the circle.

Since the length of the AB is given, the diameter of the circle is 5 cm.