Tangent and Secants If a secant and a tangent of a circle are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment.

Problem 1Use the theorem for the intersection of a tangent and asecant of a circleto solve the problems below.In the diagram on the left, the red line is a tangent, how long is it?

x = (7+5) 5x = (12) 5x = 60 x =Problem 2In the problem below, the red line is atangent of the circle, what is its length?HIDE ANSWERx = (7+9) 7x = (16) 7x = 112

Two Secants IntersectingIf two secant segments are drawn from a point outisde a circle, the product of the lengths(C+D)of one secant segment and its exteranal segment(D)equals the product of the lengths (A+B) of the other secant segment and its external segment (B).

Problem 3Use the theorem above to determine A ifB = 4, C = 8, D = 5

(A +4) 4 = (5 +8) 5(A +4) 4 = (13) 5(A +4) 4 = 65(A +4) = 65 4(A +4) = 16.25A = 16.25 4A = 12.25Problem 4Use the theorem above to determine A ifB = 8, C = 16, D = 10HIDE ANSWER(A +8) 8 = (16 +10) 10(A +8) 8 = (26) 10(A +8) 8 = 260(A +8) = 2,60 8(A +8) = 32.5A = 32.5 8A = 24.5

he twosecantsin the picture below are not drawn to scale. IfKO= 16,KJ=4, andLO= 32, what is the measure ofLM?

How to use the theorem to find sideLMKOJO=LOMOJO=KOKJJO= 16 4 = 12KOJO=LOMO16 12 = 32 MO192= 32 MO192/32=MO6 =MOLM=LOMOLM= 32 6 =26