Answer: The lengths of the segments of the other chord are 3 units and 8 units.
Step-by-step explanation: As shown in the attached figure below, let the chords AB and CD intersect inside the circle at the point O, where
AO = 4 units, OB = 6 units, Co = 3 units.
We are to find the length of OD.
We have the following theorem :
Intersecting Chord Theorem: When two chords intersect each other inside a circle, then the products of their segments are equal.
Applying the above theorem in the given circle, we must have
[tex]AO\times OB=CO\times OD\\\\\Rightarrow 4\times6=3\times OD\\\\\Rightarrow 24=3OD\\\\\Rightarrow OD=\dfrac{24}{3}\\\\\Rightarrow OD=8.[/tex]
Thus, the lengths of the segments of the other chord are 3 units and 8 units.
