Chords AB and CD intersect at point K. Find the length CD if AK = 4cm, BK = 15cm, and the length of the CK

| June 2, 2021 | education

Chords AB and CD intersect at point K. Find the length CD if AK = 4cm, BK = 15cm, and the length of the CK is 7cm less than the length DK.

Let the segment CK of the chord CD be equal to X cm, then by hypothesis, DK = (CK + 7) = (X + 7).

By the property of chords intersecting at one point, the product of the segments obtained by division at the intersection point of one chord is equal to the product of the segments of the second chord.

CK * DK = AK * ВK.

X * (X + 7) = 4 * 15.

X ^ 2 +7 * X = 60.

X ^ 2 + 7 * X – 60 = 0.

Let’s solve the quadratic equation.

D = b ^ 2 – 4 * a * c = 7 ^ 2 – 4 * 1 * (-60) = 49 + 240 = 289.

X1 = (-7 – √289) / (2 * 1) = (-7 – 17) / 2 = -24 / 2 = -12. (Doesn’t fit because <0).

X2 = (-7 + √289) / (2 * 1) = (-7 + 17) / 2 = 10/2 = 5.

CK = 5 cm.

DK = 5 + 7 = 12 cm.

CD = СK + DK = 5 + 12 = 17 cm.

Answer: The length of the chord SD = 17 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.