A chord equal to 9.6 cm is drawn in a circle 48 pi cm long. Find the length of the smaller
| June 24, 2021 | education
A chord equal to 9.6 cm is drawn in a circle 48 pi cm long. Find the length of the smaller of the arcs contracted by this chord.
Knowing the length of the circle, we determine its radius.
L = 2 * n * R = n * 48 cm.
R = n * 48 / n * 2 = 24 cm.
Let’s draw a perpendicular OH to the BC chord. CH = BC / 2 = 9.6 / 2 = 4.8 cm.
From the right-angled triangle ONS, we determine the angle of the nose.
SinNOC = CH / OC = 4.8 / 24 = 0.2.
Arcsin 0.2 ≈ 11.540.
Then the degree measure of the smaller arc BC = 2 * 11.54 = 23.080.
Determine the length of the smaller arc BC.
Arc BC = n * R * α / 180 = n * 24 * 23.08 / 180 = n * 3.077 = 9.66 cm.
Answer: The length of the smaller arc is 9.66 cm.
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