SOLUTION: A circle with centre O has a radius of 8 cm, from O to T. Segment AT is tangent to the circle. X is a point on AT. Y is the point where XO intersects the circle. Angle AOT=60 degre

Question 1101149: A circle with centre O has a radius of 8 cm, from O to T. Segment AT is tangent to the circle. X is a point on AT. Y is the point where XO intersects the circle. Angle AOT=60 degrees, and AX=XY (this length is labelled as m). Find the length of m.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

With angle AOT 60 degrees, triangle AOT is a 30-60-90 right triangle.

OT is the radius of the circle, which is 8; so AT is 8*sqrt(3) and AO is 16.

AX=XY=m; so TX = 8*sqrt(3)-m and XO = 8+m.

Then in right triangle TOX we have

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