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In the figure, TU is tangent to the circle at point U. Use the figure to answer the questions A and B. (The questions A and B are posted in the picture with the figure). ( Please Don't Repaste Another Students Answer To Answer My Questions). Will Mark Brainliest .​

In the figure TU is tangent to the circle at point U Use the figure to answer the questions A and B The questions A and B are posted in the picture with the fig class=

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semsee45

Answer:

a) UT² = ST · (RS + ST)

b) UT = 6 in

Step-by-step explanation:

  • Secant : a line that intersects the circle at two points
  • Tangent : a line that touches the circle at one point

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.

UT² = ST · (RS + ST)

Given:

  • RT = 9 in
  • ST = 4 in
  • RS + ST = RT
    ⇒ RS + 4 = 9
    ⇒ RS = 5

Using:  UT² = ST · (RS + ST)

⇒ UT² = 4(5 + 4)

⇒ UT² = 36

⇒ UT = √36 = 6 in

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