Consider △TUV in the figure below. The perpendicular bisectors of its sides are AD, BD, and CD. They meet at a single point D.
(In other words, D is the circumcenter of △TUV.)
Suppose CD = 30, UV = 142 , and UD = 78 .
Find BV ,VD , and TC .
Note that the figure is not drawn to scale.

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Sophia wrote an equation to represent the revenue of a movie theater for one day. she let x represent the number of child tickets sold and y represents the nunver of adult tickets sold. if a child ticket cost $4, an adult ticket cost $6, and the total revenue for the daybwas $420, which equation could sophia use to represent the number of chikd and adult tickets that were sold?

Answer asap and if you do you will get brainliest. catherine buys a gallon of ice cream from the store. after taking it home, she eats a fifth of a gallon of ice cream. her sister eats some of the ice cream as well. if two-thirds of the original amount of ice cream is left, then what fraction of a gallon of ice cream did her sister eat?