Question

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

Answer 1

D

Explanation:

Answer 2

Option D.

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.

`YE=FY`

`3x+7=5x-3`

`3x-5x=-7-3`

`-2x=-10`

Divide both sides by -2.

`x=5`

The value of x is 5.

We need to find the value of FY.

`FY=3x+7=3(5)+7=22`

Therefore, the correct option is D.