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A tangent is drawn from a point 17 cm from the centre of a circle of radius 8 cm. Find the length of the tangent.

1. 12 cm
2. 15 cm
3. 13 cm
4. 10 cm

Correct answer: 15 cm

Solution

The radius to the point of tangency is perpendicular to the tangent, so the radius and tangent form a right triangle with the line from the external point to the centre. Using Pythagoras, tangent length = \(\sqrt{17^2-8^2}=\sqrt{289-64}=\sqrt{225}=15\) cm.

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