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In the figure, line TU is tangent to the circle at point U. Use the figure to answer both of the questions. Show all of your work.

(a) Describe the relationship among the lengths of the segments formed by the secant, RT , and the tangent segment, TU. You may use words and/or an equation to describe.

(b) Suppose RT= 9 in. and ST = 4 in. Is it possible to find the length of TU ? If so, show how to find the length. If not, explain why not.

In the figure line TU is tangent to the circle at point U Use the figure to answer both of the questions Show all of your work a Describe the relationship among class=

Respuesta :

sqdancefan
a) By the secant rules for circles,
  RT×ST = TU²

b) Using the above relationship, fill in the given values and solve for TU.
  (9 in)×(4 in) = TU²
  TU = √(36 in²) = 6 in

Answer:

(a) The relation is RT × ST = TU²

(b) TU = 6

Step-by-step explanation:

(a) There is a secant law for circles that says the following: "if two secants are drawn to a circle from one exterior point, then the product of the external segment and the total length of each secant are equal". Applying this for the mentioned question, we have that RT × ST = TU x TU = TU² (considering that for TU case, the tangent is also a secant).

Then RT × ST = TU²

(b) Let's apply the equation in (a). RT × ST = TU² means 9 × 4 = TU²

Solving that equation, we have TU = √36 = 6

Thus TU = 6

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