The length of the other segment is longer the segment, which is equal to 7 units in the circle with radius 9 units.
What is intersecting chord theorem?
The intersecting chord theorem states that, when two chords in a circle intersect each other, then the product of their segment is equal.
Circle A has a radius of 9 units. The diameter of the circle is twice the radius of it. Thus, the diameter of the circle is,
[tex]d=9\times2\\d=18\rm\; units\\[/tex]
A chord drawn through R is partitioned by the diameter of A passing through R into two segments, one of which has a length of 7 units.
Let suppose the length of other segment is n units. Thus, the length of the two segments is 7 units and n units long.
Point R lies 5 units away from circle A and the radius of the circle is 9 units long. Thus, two segments of the diameter is,
[tex](9+5)=14\\(9-5)=4[/tex]
By the intersecting chord theorem,
[tex]7\times n=14\times4\\n=\dfrac{14\times4}{7}\\n=8\rm\; units[/tex]
Thus, the length of the other segment is longer the segment which is equal to 7 units in the circle with radius 9 units.
Learn more about the intersecting chord theorem here;
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