Question : Tangent drawn from point X touches the circle at U. O is the centre of this circle. If XU = 15 cm and OU = 8 cm, then what is the value of OX?
Option 1: 12 cm
Option 2: 19 cm
Option 3: 21 cm
Option 4: 17 cm
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Correct Answer: 17 cm
Solution :
The radius and tangent of a circle at a point of contact is always perpendicular to each other. So the angle is 90º.
According to the concept,
Since $\angle$OUX is 90°, $\triangle$XUO is a right-angled triangle at U.
OX is the hypotenuse.
Now, $OX = \sqrt{OU^2+UX^2}$
$⇒OX = \sqrt{8^2+15^2}$
$⇒OX = \sqrt{289}$
$⇒OX = 17\ \text{cm}$
Hence, the correct answer is 17 cm.
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