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

Algebra ->  Circles -> 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      Log On


   

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) About Me  (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
8%5E2+%2B+%288sqrt%283%29-m%29%5E2+=+%28m%2B8%29%5E2
64+%2B+192+-+16sqrt%283%29m+%2B+m%5E2+=+m%5E2+%2B+16m+%2B+64
192+-+16sqrt%283%29m+=+16m
12+-+sqrt%283%29m+=+m
12+=+m%28sqrt%283%29%2B1%29