# The intersection points of the chords AB and CD divides the angle D into segments CN = 4cm, and ND = 6cm.

The intersection points of the chords AB and CD divides the angle D into segments CN = 4cm, and ND = 6cm. Into what segments does point N divide the chord AB = 11cm?

Let the length of the segment NB = X cm, then the length of the segment NA = AB – X = 11 – X cm.

By the property of intersecting chords of a circle, 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.

NА * ОВ = NС * NД.

(11 – X) * X = 4 * 6.

– X ^ 2 + 11 * X = 24.

X ^ 2 – 11 * X + 24 = 0.

D = b ^ 2 – 4 * a * c = (-11) ^ 2 – 4 * 1 * 24 = 121 – 96 = 25.

X1 = (11 – √25) / (2 * 1) = (11 – 5) / 2 = 6/2 = 3.

X2 = (11 + √25) / (2 * 1) = (11 + 5) / 2 = 16/2 = 8.

NB = 3 cm.

NA = 11 – 3 = 8 cm.

Answer: Point N divides chord AB into 3 cm and 8 cm segments. 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.