The measure of the length of a chord of a circle is 16 cm and its distance from the center of the circle is 6 cm the radius of circle is
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A chord is 16cm from the center of a circle with radius 10 cm. What is the length of the chord?
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2 ANSWERS
Martyn Hathaway, BSc Mathematics, University of Southampton (1986)
Answered Aug 14, 2018 · Author has 1.7kanswers and 664.7k answer views
A chord is 16cm from the center of a circle with radius 10 cm. What is the length of the chord?
Any chord of a particular circle must be within that circle and hence must be nearer to the centre of the circle than the perimeter, i.e. the distance must be less than the radius.
As your ‘chord’ is 16 cm from the centre of the circle, it is clearly not within the circle, so it is a not a chord of the circle.
The obvious conclusion is that you mistyped the question. One possibility is that the chord is 6 cm from the centre.
The angles OCA and OCB are right angles, thus we can use Pythagoras to calculate the lengths AC and AB.
OA2=OC2+AC2⇒102=62+AC2⇒AC2=64⇒AC=8" role="presentation" style="margin: 0px; padding: 0px; outline: 0px; display: inline-table; font-style: normal; font-weight: normal; line-height: normal; font-size: 14px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;">OA2=OC2+AC2⇒102=62+AC2⇒AC2=64⇒AC=8OA2=OC2+AC2⇒102=62+AC2⇒AC2=64⇒AC=8
You should realise that BC is the same length as AC.
The length of the chord is clearly AC + BC = 16
Answer: 16 cm
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Perhaps you have mixed up the word order? Perhaps you should be finding the distance of the chord given a length of 16 cm? In which case, the answer is 6 cm.
646 Views · Answer requested by Saleh Idriss
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OTHER ANSWERS
Bill Hoolan, former Retired Math Teacher
Answered Jun 30, 2018 · Author has 212answers and 14.9k answer views
This is impossible. The chord would be outside the circle.
.