∆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
To find RT, we first need to find the radius of circle P. Since the diameter is 24 inches, the radius is half of that, which is 12 inches.
Now, we know that angle I is 60° and that angle I is an inscribed angle, which means its measure is half of the measure of the arc it intercepts. So, the arc intercepted by angle I is 2*60° = 120°.
Since the arc intercepted by angle I is 120°, the arc of circle P that RT cuts out is 360° - 120° = 240°.
Now, we can use the formula for the circumference of a circle to find the length of the arc that RT cuts out:
Circumference = 2 * π * radius
Arc length = (arc angle/360) * Circumference
Arc length = (240/360) * 2 * π * 12
Arc length = (2/3) * 24 * π
Arc length = 16 * π
Therefore, the length of RT is approximately 16 * π = 50.27 inches. Rounded to the nearest hundredth, RT is 50.27 inches.