Chord 4, root 2 cm, pulls a 90-degree arc. Find the length of the circle
| September 30, 2021 | education
From the center of the circle, draw segments OA and OB to the edges of the chord. The degree measure of the formed central angle AOB is equal to the degree measure of the arc on which it rests. Angle AOB = 900, then triangle AOB is equilateral and right-angled.
By the Pythagorean theorem, we determine the lengths of the legs OA and OB.
AB ^ 2 = OA ^ 2 + OB ^ 2 = 2 * OA ^ 2.
(4 * √2) ^ 2 = 2 * OA ^ 2.
OA ^ 2 = 3 ^ 2/2 = 16.
ОА = R = 4 cm.
Determine the length of the circle. L = 2 * n * R = 2 * n * 4 = 8 * n cm.
Answer: The circumference is 8 * n cm.
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