SOLUTION: A circle with center O has a radius of 12cm. The chord AB subtends at an angle of 75 degrees at the center. The tangents to the circle at A and B meet at P. Find the length of BP.

Question 821189: A circle with center O has a radius of 12cm. The chord AB subtends at an angle of 75 degrees at the center. The tangents to the circle at A and B meet at P.
Find the length of BP.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A circle with center O has a radius of 12cm.
The chord AB subtends at an angle of 75 degrees at the center.
The tangents to the circle at A and B meet at P.
Find the length of BP.
:
draw this out. draw a line from O to P, now you have right triangle BPO
The OP line bisects the 75 degrees, so angle BOP is 37.5 degrees.
Line BP is opposite this angle,
Line OB is the radius, 12 cm
We can use the tangent here
tan(37.5) =
BP = .767327 * 12
BP = 9.208 cm
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