Find the length of the chord given that the circle's diameter and the subtended angle

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A chord of a circle subtends an angle of 89 degrees at its centre. Find the length of the chord given that the circle's diameter is 11.4 cm.

The problem I have here is that I can't visualise this question. I've tried drawing it but gets all messy and I get confused so can someone please draw the diagram for me? That's all I need because I can work from there on after.

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3 Answers

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This is how I interpret the problem:

The task is to find the length of the red line.

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There is a formula for that,

$$ 2 \cdot 5.7 \cdot \sin \left(\frac{89 \pi }{360} \right) = 7.9903656130183 $$

Where A is the angle in radians and r is the radius.

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The way to solve it is : Use the Formula: 2r sin A/C

$OA = OB = 5.7$cm as it is the radius. So, you would get:

$2 \cdot 5.7 \cdot \sin \left(\frac{89 \pi }{360} \right) = 7.9903656130183$

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