Question

Point A is inside triangle E D F. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A L, A M, and A N. The length of A E is 10 and the length of A D is 2 n + 4. What value of n would make point A the circumcenter? 2 3 4 5

Answer 1

Option B. 3 is the answer.

Explanation:

To draw a circumcenter of a triangle we draw the perpendicular bisectors of the the sides of the triangle first.

Intersection point of these perpendiculars drawn is the circumcenter of the circle.

Distances of the circumcenter to the vertices are same, that means distance of circumcenter from the vertex is the radius of the circle.

Therefore, length of AE and AD will be same in measure.

AE = AD

2n + 4 = 10

2n = 10 - 4

2n = 6

n = 3

Therefore, Option B. 3 is the answer.