Question : A circle of radius 5 cm and the length of tangent drawn from a point $X$ outside the circle is 12 cm. The distance of the point $X$ from the centre of the circle is:
Option 1: 12 cm
Option 2: 11 cm
Option 3: 10 cm
Option 4: 13 cm
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Correct Answer: 13 cm
Solution :
Let $OT$ = 5 cm and $XT$ = 12 cm
We know the theorem states that in a circle, the radius is perpendicular to the tangent at the point of contact.
Use the Pythagorean theorem
In $\triangle OTX$
$OX^2 = OT^2 + XT^2$
⇒ $OX^2 = 5^2 + 12^2 = 25 + 144 = 169$
⇒ $OX = \sqrt{169} = 13$ cm
Hence, the correct answer is 13 cm.
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