# A circle of radius 14cm has a chord of length 12cm. What is the shortest distance from the chord to the centre of the circle?Geometry of Circles. the answer is the square root of 160cm. how do i...

A circle of radius 14cm has a chord of length 12cm. What is the shortest distance from the chord to the centre of the circle?

Geometry of Circles. the answer is the square root of 160cm. how do i get to the answer.

beckden | High School Teacher | (Level 1) Educator

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The chord is closest to the center at a right angle to the center.  Radius = 14.  Chord length = 12

So the answer is `sqrt(14^2 - 6^2) = sqrt(196-36) = sqrt(160) = 4sqrt(10) cm`

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Given radius of the circle is 14 cm and chord length is 12 cm.The shortest distance from the center of the circle to chord means the distance from the center of the circle to center of the chord.The hypotenuse of triangle is 14 cm and adcent side is half the chord length(6cm).Let x is the shortest distance.

The shortest distance from the chord to center of the circle is

x^2+6^2=(14)^2

x=square root of 160cm

The shortest distance from the chord to center of the circle is "square root of 160 cm".