Question : The lengths of the two adjacent sides of a rectangle inscribed in a circle are 5 cm and 12 cm, respectively. Then, the radius of the circle will be:
Option 1: 6 cm
Option 2: 6.5 cm
Option 3: 8 cm
Option 4: 8.5 cm
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Correct Answer: 6.5 cm
Solution :
The lengths of the two adjacent sides of a rectangle inscribed in a circle are 5 cm and 12 cm, respectively.
Since it is a rectangle,
Diagonal = $\sqrt{12^{2}+5^{2}}$ = $\sqrt{144+25}$ = $\sqrt{169}$ = 13 cm
Here, the diagonal of the rectangle = diameter of the circle
So, the radius of the circle = $\frac{13}{2}$ = 6.5 cm
Hence, the correct answer is 6.5 cm.
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