Two chords AB and CD are drawn in the circle, intersecting at the point K, KC = 6 cm

univerkov | February 6, 2021 | education

Two chords AB and CD are drawn in the circle, intersecting at the point K, KC = 6 cm, AK = 8 cm, BK + DK = 28 cm. Find the product of BK and DK.

We apply the property of intersecting chords, according to which the product of the lengths of the segments of one chord formed at the intersection is equal to the product of the lengths of the segments of the other chord.

Let the length of the segment BK = X cm, then DK = (28 – X) cm.

DC * CK = AK * ВK.

(28 – X) * 6 = 8 * X.

168 – 6 * X = 8 * X.

14 * X = 168.

X = BK = 168/14 = 12 cm.

DK = 28 – 12 = 16 cm.

Then ВK * DK = 12 * 16 = 192.

Answer: The product of the segments is 192.

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.