Point Y is the circumcenter of ΔDEF. Point Y is the circumcenter of triangle D E F. Lines are drawn from the points of the triangles to point Y. Lines are drawn from point Y to the sides of the triangle to form right angles and line segments Y L, Y M, and Y N. The line segments cut the sides of the triangles into 2 equal parts. The length of F Y is 3 x + 7 and the length of Y E is 5 x minus 3. Find FY. a. 5 b. 11 c. 17 d. 22

Accepted Solution

Answer:Option D.Step-by-step explanation:Given information: Point Y is the circumcenter of ΔDEF, FY=3x+7 and YE=5x-3.It the perpendicular bisectors of the sides of a triangle intersect at point P, then P is the circumcenter of the triangle and it is equidistant from the three vertices.Since Y is the circumcenter of ΔDEF, So by using the definition of circumcenter we can say that YE is equal to FY.[tex]YE=FY[/tex][tex]3x+7=5x-3[/tex][tex]3x-5x=-7-3[/tex][tex]-2x=-10[/tex]Divide both sides by -2.[tex]x=5[/tex]The value of x is 5.We need to find the value of FY.[tex]FY=3x+7=3(5)+7=22[/tex]Therefore, the correct option is D.