The chord perpendicular to the diameter of the circle divides the diameter into 2 segments 16 cm and 4 cm.

| March 7, 2021 | education

The chord perpendicular to the diameter of the circle divides the diameter into 2 segments 16 cm and 4 cm. Find the length of the chord and the distance from the chord to the center of the circle.

Segment СK = DK, since the chord is perpendicular to the diameter and is divided by it into equal segments.

By the property of chords intersecting at one point, the product of the lengths of the segments formed at the intersection of one chord is equal to the product of the lengths of the segments of the other chord.

AK * ВK = СK * DK.

Let CK = DK = X cm.

4 * 16 = X * X.

X2 = 64.

X = 8 cm, then the length of the chord СD = 2 * 8 = 16 cm.

Let the segment OK = Y cm, then:

AK + U = ВK – U.

4 + Y = 16 – Y.

2 * Y = 16 – 4 = 12.

Y = 12/2 = 6 cm.

Answer: The chord length is 16 cm, the distance from the chord to the center of the circle is 6 cm.



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