The diameter of the circle is 200 mm, the chord is 120 mm. How far from the center does it stand?

| August 14, 2021 | education

By the property of chords that intersect at one point, the product of the segments formed by the intersection of one chord is equal to the product of the segments of the other chord.

AM * CM = BM * DM.

Since the chord AC is the diameter of the circle, then when the ВD intersects at a right angle, it will divide it in half ВM = DM = 120/2 = 60 cm.

Let CM = X cm, then AM = AC – X = (200 – X).

(200 – X) * X = 60 * 60.

X2 – 200 * X + 3600 = 0.

Let’s solve the quadratic equation.

D = b2 – 4 * a * c = (-200) ^ 62 – 4 * 1 * 3600 = 40,000 – 14400 = 25600.

X1 = (200 – √25600) / (2/1) = (200 – 160) / 2 = 40/2 = 20.

X2 = (200 + √25600) / (2/1) = (200 + 160) / 2 = 360/2 = 180.

If CM = 20 cm, then OM = R – CM = 100 – 20 = 80cm.

If CM = 180 cm, then OM = CM – R = 180 – 100 = 80cm.

Answer: The distance from the chord to the center of the circle is 80 cm.



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