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If triangle AOB is equilateral, O is the midpoint of AC, and the radius of semicircle ABC is 6, what is the length of line segment BC?
1. 3* (3^1/2)
2. 6*(2^1/2)
3. 6*(3^1/2)
4. 6*(5^1/2)
5. 12

Radius is 6 so AC = 12; AB = 6 (equilateral triangle). So BC = 12^2 - 6^2 = 108 ^ 1/2 = 6 * 1/3^2

Another way to solve this is to split the equilateratal triangle into two 30-60-90 triangles. This will give you the height of a right triangle with segment BC as the hypotnuse.

If triangle AOB is equilateral, O is the midpoint of AC, and the radius of semicircle ABC is 6, what is the length of line segment BC? 1. 3* (3^1/2) 2. 6*(2^1/2) 3. 6*(3^1/2) 4. 6*(5^1/2) 5. 12

Radius is 6 so AC = 12; AB = 6 (equilateral triangle). So BC = 12^2 - 6^2 = 108 ^ 1/2 = 6 * 1/3^2