Question

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.

Answer 1

The tangent secant theorem says

PR × PS = PQ²

4 × (4+5) = PQ²

36 = PQ²

PQ=6

Answer: 6