Discussion
The diameter of a circle is 10 cm. "P" is the point lying outside the circle. From that point "P" two tangents are drawn to the circle. The length of each tangent is 12 cm. What is the distance between "P" and the centre of the circle.
Answer: B
The distance is 13 cm.
A tangent is perpendicular to the radius at the point of contact, so the radius, the tangent and the line from P to the centre form a right-angled triangle. The radius is half the diameter, 5 cm:
\[ OP = \sqrt{5^{2} + 12^{2}} = \sqrt{169} = 13\ \text{cm} \]
Using the diameter, 10 cm, as a side instead of the radius gives about 15.6 cm, near the 15 cm option; 12 cm is just the tangent length, and 10 cm the diameter.
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