Circle Relationships

If WX=6, YX=12, and VX=8, find the length of ZX

If LJ=5 and JM=15, find the value of LK

QS is a tangent to circle P. Find QS.

In the figure shown below, quadrilateral TAEO is circumscribed around circle D. The midpoint of TA is R, and HO ≅ PE. If AP = 10 and EO = 12, what is the perimeter of quadrilateral TAEO?

In the diagram below, secants RST and RQP, drawn from point R, intersect circle O at S, T, Q, and P. If RS = 6, ST = 4, and RP = 15, what is the length of RQ?

In the diagram shown below, PA is tangent to circle T at A, and secant PBC is drawn where point B is on circle T. If AP = 4 and PB=2 , what is the length of BC?

In the diagram below, chords PQ and RS of circle O intersect at T. Which relationship must always be true?

In the diagram below of circle O, chords JT and ER intersect at M. If EM = 8 and RM = 15, the lengths of JM and TM could be

In circle O, secants ADB and AEC are drawn from external point A such that points D, B, E, and C are on circle O. If AD = 8, AE = 6, and EC is 12 more than BD, the length of BD is

HINT: draw a diagram