A 40 cm long chord is drawn in the circle, which is 15 cm from the center of the circle. Find the length of a circle.
| May 24, 2021 | education
From the center O of the circle, draw the segments OA and OB to the edges of the chord AB.
The ABO triangle is isosceles, since A and OB are the radii of the circle, then the height OH drawn to the chord from the point O divides the chord AB in half. AH = BH = AB / 2 = 20 cm.
From the right-angled triangle OAH, by the Pythagorean theorem, we determine the length of the hypotenuse OA.
OA ^ 2 = AH ^ 2 + OH ^ 2 = 400 + 225 = 625.
ОА = R = 25 cm.
Determine the length of the circle.
L = 2 * n * R = 2 * 3.14 * 25 = 157 cm.
Answer: The circumference is 157 cm.
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