Question : If AB = 5 cm, AC = 12 cm, and AB$\perp$ AC, then the radius of the circumcircle of $\triangle ABC$ is:
Option 1: 6.5 cm
Option 2: 6 cm
Option 3: 5 cm
Option 4: 7 cm
Correct Answer: 6.5 cm
Solution :
Given: $AB = 5$ cm; $AC = 12$ cm and $AB \perp AC$
$BC$ = Diameter
In $\triangle ABC$,
$BC = \sqrt{AB^2 + AC^2}$
$BC = \sqrt{5^2 + 12^2} = \sqrt{25 + 144}$
$BC = \sqrt{169} = 13 \;cm$
$\therefore OB$ is the radius = $\frac{BC}{2}=\frac{13}{2}=6.5$ cm
Hence, the correct answer is $6.5$ cm.
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