Question : Find the length of a tangent drawn to a circle with a radius 8 cm from a point 17 cm from the centre of the circle.
Option 1: 14 cm
Option 2: 12 cm
Option 3: 15 cm
Option 4: 10 cm
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Correct Answer: 15 cm
Solution :
Radius of circle, $PB$ = 8 cm
Distance of a point from the centre from which the tangent is drawn to the circle, $PA$ = 17 cm
Since tangent is perpendicular to the radius, $\angle PBA=90^{\circ}$
By Pythagoras in $\triangle PBA$,
Length of the tangent, $AB$ = $\sqrt{17^2-8^2}$ = 15 cm
Hence, the correct answer is 15 cm.
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