Question : $\triangle$ XYZ is a right-angled triangle and $\angle$Y = 90° If XY = 2.5 cm and YZ = 6 cm, then the circumradius of $\triangle$XYZ is:
Option 1: 6.5 cm
Option 2: 3.25 cm
Option 3: 3 cm
Option 4: 2.5 cm
Correct Answer: 3.25 cm
Solution :
Given: XYZ is a right-angled triangle and $\angle$Y = 90°, where XY = 2.5 cm and YZ = 6 cm.
Let the hypotenuse of the triangle be $h$ cm.
So, $h^2=6^2+(2.5)^2$
⇒ $h=\sqrt{42.25}$
⇒ $h=6.5$ cm
We know,
The circumradius of a right-angled triangle is half of its hypotenuse.
So, the circumradius = $\frac{6.5}{2}$ = 3.25 cm
Hence, the correct answer is 3.25 cm.
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