SOLUTION: a chord is drawn away from the centre of a circle of radius 5cm.calculate the length of the chord

Question 1135519: a chord is drawn away from the centre of a circle of radius 5cm.calculate the length of the chord

Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
based on the following reference, i think you also need the central angle formed by the chord.

https://www.ck12.org/trigonometry/Length-of-a-Chord/lesson/Length-of-a-Chord-TRIG/

the reference uses radians, but the same concept applies with degrees.

otherwise, the length of the chord could be any length up to the length of the diameter which would, in this case, be equal to 10.

if you have the central angle, then you can find the length of the chord, because you can split the chord in half by taking a line segment from the center of the circle to intersect with the chord at a right angle.

this splits the chord in half.

it also forms a two right triangles, each of which will have an angle equal to half the central angle.

then you can find the length of half the chord by using sine of half the angle equals half the length of the chord divided by the radius.

solve for half the length of the chord to be equal to the radius * half the central angle.

multiply that by two and you have the length of the chord.

two examples:

the central angle is 90 degrees.

the central angle is 140 degrees.

see the attached diagram and formula, assuming the radius is 5 centimeters.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The problem is poorly worded, so its meaning is unclear.

"a chord is drawn away from the centre of a circle..."

That sounds as if you are drawing a chord starting at the center of the circle and moving away from it. But a chord connects two points on the circle. It doesn't pass through the center of the circle unless it is a diameter.

If you have a chord in a circle with known radius, then to find the length of the chord you need to know either the central angle or the distance of the chord from the center of the circle.
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