The length of a tangent from an external point to a circle is 5 \sqrt3 unit. If radius of the circle is 5 units, then the distance of the point from the circle is

SSC CGL 19 Oct 2014 Shift 2 Paper

Question : 137 of 200

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The length of a tangent from an external point to a circle is 5

√3

unit. If radius of the circle is 5 units, then the distance of the point from the circle is

Solution:

AB = 5

√3

units
OA = 5 units
∠ OAB = 90°
∴ OB =

√{AB^2+OA^2}

√{(5√3)^2+5^2}

√{75+25}

√{100}

= 10 units
∴ BC = OB – OC
= 10 – 5 = 5 units

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