Question

5. Circle A has a radius of 9 units . Point R lies 5 units away from A. 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. Is the length of the other segment longer or shorter than 7 units ? Justify your answer.

Answer 1

Answer:

The length of the other segment is longer than 7 units

Step-by-step explanation:

we know that

The intersecting chords theorem states that the products of the lengths of the line segments on each chord are equal

see the attached figure to better understand the problem

Remember that the diameter of the circle is two times the radius

$D=2(9)=18\ units$

Let

x ----> the length of the other segment

so

$(9+5)(4)=(7)(x)$

$56=7x\\x=8\ units$

therefore

The length of the other segment is longer than 7 units