Given:AE = 21, EB = 14, DE : EC = 3 : 1. Find:DE and EC

Question

Consider the following theorem.

If two chords intersect within a circle, then the product of the lengths of the segments (parts) of one chord is equal to the product of the lengths of the segments of the other chord.

O is the center of the circle.

Given:AE = 21

EB = 14

DE : EC = 3 : 1

Find:DE and EC

Answer 1

If EC is x, the DE = 3x

By the theorem:

3x * x = 21 * 14

3x^2 = 294

x^2 = 98

x = 9.9

EC = 9.9 and DE = 29.7