(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.

Answer:Part a) minor arc: XY; major arc: XVYPart b) [tex]248\°[/tex]Part c) The tangent line is UV and the secant line is XYPart d) [tex]UV=6\sqrt{5}\ units[/tex]  or  [tex]UV=13.42\ units[/tex]Step-by-step explanation:Part a) we know thatThe major arc is the larger arc joining two points on the circumference of a circle. Is an arc larger than a semicircle.The sum of major and minor arcs is the whole circle, 360°In this problem, possible major arcs areVYX, VXY, XVYand the corresponding minor arcs areVX, VY, XYPart b) we know thatThe sum of major and minor arcs is the whole circle, 360°soLetx------> measure minor arcy-------> measure of major arc[tex]x+y=360\°[/tex]we have[tex]x=112\°[/tex]substitute[tex]112\°+y=360\°[/tex][tex]y=360\°-112\°=248\°[/tex]Part c) we know thatA tangent line intersects a circle at exactly one point. In this problem The tangent line is UVA secant line intersects a circle in two points. In this problem The secant line is XY Part d) we know thatThe Intersecting Secant Theorem States: When two secant lines intersect each other outside a circle, the products of their segments are equalso[tex]UV*UV = UX*UY[/tex][tex]UV^{2}  = 9*(9+11)[/tex][tex]UV^{2}  = 180[/tex][tex]UV=\sqrt{180}\ units[/tex]Simplify[tex]UV=6\sqrt{5}\ units[/tex]  or  [tex]UV=13.42\ units[/tex]