1. given the following diagram. (a) name the minor arc name the major arc (b) if the minor arc is 112°, what is the measure of the rest of the circle arc length? (c) which line is the tangent? which line is the secant? (d) if xy is 11 and ux is 9, what is the length of uv? show all work or no credit.

a) XY , XVY

b) 248°

c) UV , UY

d) 6√5 = 13.42

Step-by-step explanation:

a) The minor arc is XY

   The major arc is XVY

b) ∵ The measure of the minor arc is 112°

    ∵ The measure of the circle is 360°

    ∴ The measure of the rest arc = 360 - 112 = 248°

c) UV is the tangent to the circle

   UY is the secant to the circle

d) ∵ UV is a tangent to the circle at V

    ∵ UY is a secant to the circle

    ∴ (UV)² = (UX) × (UY)

    ∵ UX = 9 and XY = 11 ⇒ ∴ UY = 11 + 9 = 20

     ∴ (UV)² = 9 × 20 = 180

      ∴ UV = √180 = 6√5 = 13.42

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