Question : PX is a tangent drawn from point X, that touches the circle at P. O is the centre of the circle. The radius of this circle is 10 cm and OX = 26 cm. What is the length of PX?
Option 1: 24.5 cm
Option 2: 24 cm
Option 3: 23.5 cm
Option 4: 25 cm
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Correct Answer: 24 cm
Solution :
In a circle, the radius is perpendicular to the tangent at the point of tangency. Therefore, in this case, OP is perpendicular to PX. This forms a right-angled triangle OPX.
$OX^2 = OP^2 + PX^2$
Substituting the given values,
$⇒26^2 = 10^2 + PX^2$
$⇒PX = \sqrt{26^2 - 10^2} = \sqrt{576} = 24 \text{ cm}$
Hence, the correct answer is 24 cm.
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