In the diagram, PQ¯¯¯¯¯¯¯¯
is tangent to the circle at point Q,
and secant PS¯¯¯¯¯¯¯
intersects the circle at points R
and S.
The lines intersect outside the circle at point P.
A circle with no center shown. Points S, R, and Q lie on the circle. Secant P S and tangent P Q are described in the text. Segment R S equals 5 and segment P R equals 4. What is the length of PQ¯¯¯¯¯¯¯¯?
Enter the correct value.
The length of PQ¯¯¯¯¯¯¯¯ is 9.
This can be calculated using the formula for the product of segments of secants:
PS * PR = PQ * PR
Substitute in the given values:
5 * 4 = PQ * 4
20 = PQ * 4
PQ = 20 / 4
PQ = 5
Therefore, the length of PQ¯¯¯¯¯¯¯¯ is 9.