Question : In a triangle PQR, $\angle$Q = 90°. If PQ = 12 cm and QR = 5 cm, then what is the radius (in cm) of the circumcircle of the triangle?
Option 1: $5$
Option 2: $6$
Option 3: $6.5$
Option 4: $6\sqrt2$
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Correct Answer: $6.5$
Solution :
Given: In a triangle PQR, $\angle$Q=90°, PQ = 12 cm, and QR = 5 cm.
Let the hypotenuse of the triangle be $h$ cm.
So, $h^2=12^2+5^2$
⇒ $h=\sqrt{169}$
⇒ $h=13$ cm
We know,
The circumradius of a right-angled triangle is half of its hypotenuse.
So, the circumradius = $\frac{13}{2}$ = 6.5 cm
Hence, the correct answer is $6.5$.
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