The chord crosses the second chord and divides it into segments of 6 cm and 16 cm and, in turn, dividing

The chord crosses the second chord and divides it into segments of 6 cm and 16 cm and, in turn, dividing it into segments in a ratio of 3: 2. Find the length of the first chord is geometry

Given: AB and CK are chords. AB crosses CK at point E; AE = 6 cm; EB = 16 cm; CE: EK = 3: 2.
Find SC -?
Solution:
If the chord AB intersects the CK at the point E, then CE * EK = AE * EB. Therefore CE * EK = 6 * 16; CE * EK = 96. Let one part x cm, then CE = 3x, and EK = 2x cm. We make the equation 3x * 2x = 96; 6x squared = 96; x per frame = 96: 6; x squared = 16; x = 4. Then CE = 3 * 4 = 12 cm and EK = 2 * 4 = 8 cm. and СK = 12 + 8 = 20 cm.
Answer: 20 centimeters.