In the diagram, secant AP¯¯¯¯¯¯¯¯
intersects the circle at points A
and B,
and secant CP¯¯¯¯¯¯¯¯
intersects the circle at points C
and D.
The lines intersect outside the circle at point P.
A circle with no center shown and two secants as described in the text. Points A, B, D and C lie on the circle. Segment B P equals 6, segment C D equals 7, and segment D P equals 5. What is the length of AP¯¯¯¯¯¯¯¯?
Enter the correct value
To find the length of AP¯¯¯¯¯¯¯¯, we first need to find the length of CP¯¯¯¯¯¯¯¯ by using the segment addition postulate: BD + DP = BP.
So, 7 + 5 = 6 + CP
12 = 6 + CP
CP = 6
Now, we can find the length of AC¯¯¯¯¯¯¯¯ using the segment addition postulate: CP + CD = AC
So, 6 + 7 = AC
13 = AC
Finally, we can find the length of AP¯¯¯¯¯¯¯¯ using the segment addition postulate: AC = AP
Therefore, the length of AP¯¯¯¯¯¯¯¯ is 13.
So, the correct value for the length of AP¯¯¯¯¯¯¯¯ is 13.