Question

Two chords intersect inside a circle. the lengths of the segment of one chord are 4 and 6. the lengths of the segments of the other chord are 3 and _
7
8
9

Answer 1

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

$AO\times OB=CO\times OD\\\\\Rightarrow 4\times6=3\times OD\\\\\Rightarrow 24=3OD\\\\\Rightarrow OD=\dfrac{24}{3}\\\\\Rightarrow OD=8.$

Thus, the lengths of the segments of the other chord are 3 units and 8 units.

Answer 2

Answer:

  8

Step-by-step explanation:

The product of the segment lengths of one chord is equal to the product of the segment lengths of the other chord:

  4 · 6 = 3 · 8