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, as described in the text. Segment A P equals 10, segment B P equals 12, and segment D P equals 8.What is the length of CP¯¯¯¯¯¯¯¯?
Responses
10
10
6.7
6 point 7
9.6
9 point 6
15
To find the length of CP¯¯¯¯¯¯¯¯, we can use the intersecting chords theorem. This theorem states that the product of the segments of one chord is equal to the product of the segments of the other chord.
Therefore, AP × BP = CP × DP
10 × 12 = CP × 8
120 = CP × 8
CP = 120 / 8
CP = 15
Therefore, the length of CP¯¯¯¯¯¯¯¯ is 15.