∆TRI is inscribed in circle P whose diameter is 24 inches, and m∠I
= 60°.
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Find RT, in inches. Round to the nearest hundredth, if necessary.
First, we need to determine the length of the radius of circle P. Since the diameter is 24 inches, the radius is half of that, which is 12 inches.
Next, we know that an inscribed angle is equal to half the measure of the central angle that intercepts the same arc. In this case, m∠I = 60°, so the central angle ∠POI is 120°.
Since triangle TRI is isosceles (radii of a circle are always equal), we have another central angle ∠ORI that is also 120°.
Now, we can use the Law of Cosines to find the length of RT:
RT^2 = RO^2 + OT^2 - 2(RO)(OT)cos(120°)
RT^2 = 12^2 + 12^2 - 2(12)(12)cos(120°)
RT^2 = 144 + 144 - 288(-0.5)
RT^2 = 288 + 144
RT^2 = 432
RT = √432
RT ≈ 20.78 inches
Therefore, RT is approximately 20.78 inches.