Points $T$ and $U$ lie on a circle centered at $O$, and point $P$ is outside the circle such that $\overline{PT}$ and $\overline{PU}$ are tangent to the circle. If $\angle TPO = 33^{\circ}$ and $PT = 10$, then what is the radius of the circle?
T
10
O 33 P
U
Connect OT , TP and OP
Triangle OTP will be a right triangle with angle OTP = 90° and OT the radius of the circle and angle POT = 90 - 33 = 57°
By the Law of Sines
PT / sin 57° = OT / sin 33°
10 sin 33° / sin 57° = OT ≈ 6.5 = circle radius