In circle PP, mangle, Q, P, R, equals, 144, degrees∠QPR=144 ∘ and the length of arc, Q, R, equals, 4, pi QR⌢ =4π. Find the length of start overline, P, Q, end overline PQ .
Question
In circle PP, mangle, Q, P, R, equals, 144, degrees∠QPR=144 ∘ and the length of arc, Q, R, equals, 4, pi QR⌢ =4π. Find the length of start overline, P, Q, end overline PQ .
Solution
To solve this problem, we need to use the properties of circles and the relationship between the arc length, the radius, and the central angle.
Step 1: Find the radius of the circle. The formula for the length of an arc is given by L = rθ, where L is the arc length, r is the radius, and θ is the central angle in radians.
Given that the length of arc QR is 4π and the measure of ∠QPR is 144 degrees, we first need to convert the angle from degrees to radians.
1 radian = 180/π degrees, so 144 degrees = 144 * π/180 = 4π/5 radians.
Now we can use the formula L = rθ to find the radius:
4π = r * 4π/5 r = 5
Step 2: Find the length of PQ. The length of a line segment from the center of a circle to a point on the circle (like PQ) is simply the radius of the circle.
So, the length of PQ is 5 units.
Similar Questions
In circle MM, mangle, N, M, O, equals, 70, degrees∠NMO=70 ∘ and the area of the shaded sector = start fraction, 7, divided by, 4, end fraction, pi 47 π. Find the length of start overline, M, N, end overline MN .
Given the circle below with chords start overline, Q, R, end overline QR and start overline, S, T, end overline ST . Find the length of start overline, Q, U, end overline QU . Round to the nearest tenth if necessary.
Given the circle below with secants start overline, E, F, G, end overline EFG and start overline, I, H, G, end overline IHG . If F, G, equals, 25, comma, H, G, equals, 22FG=25,HG=22 and I, HIH is 88 more than E, FEF, find the length of start overline, I, H, end overline IH . Round to the nearest tenth if necessary.
In circle UU, mangle, V, U, W, equals, 20, degrees∠VUW=20 ∘ and the area of shaded sector = start fraction, 25, divided by, 18, end fraction, pi 1825 π. Find the length of arc, V, W VW⌢ . Express your answer as a fraction times piπ.
In circle JJ, mangle, K, J, L, equals, 160, degrees∠KJL=160 ∘ and the area of shaded sector = start fraction, 16, divided by, 9, end fraction, pi 916 π. Find the length of arc, K, L KL⌢ . Express your answer as a fraction times piπ.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.