Question

what value of n would make point a the circumcenter?
2
3
4
5

Explanation:

Step1: Recall circumcenter property

The circumcenter of a triangle is equidistant from all vertices. So, \( AE = AD \) (since \( A \) is circumcenter, distances to vertices \( E \) and \( D \) should be equal). Given \( AE = 10 \) and \( AD = 2n + 4 \), set them equal: \( 2n + 4 = 10 \).

Step2: Solve for \( n \)

Subtract 4 from both sides: \( 2n = 10 - 4 = 6 \). Then divide by 2: \( n = \frac{6}{2} = 3 \).

Answer:

3 (corresponding to the option "3")