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| Math Central | Quandaries & Queries |
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Beary, a student: AOC is a diameter of circle O. Line AB is 12, and lines OA and OC (the radii) are 10. Find the length of line BO and chord BC. |
Hi Beary,
Remember that if O is the centre then OB will also be a radius of 10.
You first need to solve for angle θ using the law of cosine states:
For any triangle with side lengths a, b and c,
c2 = a2 + b2 - 2ab cos C
where angle C is the angle opposite side length c.
In your case, side AB is opposite to θ.
Next solve for α which we know equals 180- θ since it makes a straight angle with θ. Use the value of α and the law of cosines again to solve for side BC.
Hope this helps,
Janice
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