Question : A tangent is drawn from an external point 'A' to a circle of radius 12 cm. If the length of the tangent is 5 cm, then the distance from the centre of the circle to point 'A' is:
Option 1: 17 cm
Option 2: 9 cm
Option 3: 7 cm
Option 4: 13 cm
Correct Answer: 13 cm
Solution :
A tangent at any point of a circle is perpendicular to the radius through the point of contact.
According to the Pythagorean theorem, we have:
$OA^2 = OP^2 + PA^2$
Substituting the given values, we get:
$OA^2 = 12^2 + 5^2 = 144 + 25 = 169$
⇒ $OA = \sqrt{169} = 13 \text{ cm}$
Hence, the correct answer is 13 cm.
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