Study the diagram, where AB¯¯¯¯¯¯¯¯
and CD¯¯¯¯¯¯¯¯
are chords that intersect inside of the circle at point P,
which is not the center.
A circle, with no center shown, and two chords as described in the text. Segment A P equals 10, segment B P equals x, segment C P equals 8, and segment D P equals 3 plus x.What is the length of x?
Responses
6
6
14
14
8
8
11
To find the length of x, we can use the intersecting chord theorem which states that when two chords intersect inside a circle, the product of the segments of one chord is equal to the product of the segments of the other chord.
So, AP * BP = CP * DP
10 * x = 8 * (3 + x)
10x = 24 + 8x
2x = 24
x = 12
Therefore, the length of x is 12.