Question

What value of n would make point A the circumcenter?

1. 2
2. 3
3. 4
4. 5

Answer 1

Answer:

The correct option is 2. The value of n is 3.

Step-by-step explanation:

Circumcenter is the point, where the perpendicular bisectors of a triangle intersect each other.

Circumcenter is also known as the center of the triangle. The distance from circumcenter to each vertex are same.

In triangle DEF, if A is the circumcenter.

$AE=AD$

$10=2n+4$

Subtract 4 from both sides.

$10-4=2n$

$6=2n$

Divide both sides by 2.

$3=n$

Therefore the value of n is 3 and option 2 is correct.

Answer 2

Answer:

Option 2 is true

Step-by-step explanation:

We have to find the value of n for which point A becomes circumcenter.

Circumcenter: It is that point where perpendicular bisectors of triangle intersects.

The circumcenter  is also knows as center of triangle.

Circumcenter is at equal distance from each vertex of triangle.

If point A is circumcenter then

AE=AD

We have AE=10 units

AD=2n+4

Substitute the value

10=2n+4

$2n=10-4$

By subtraction property of equality

$2n=6$

$n=\frac{6}{2}=3$

Hence, the value of n is 3 would make point A the circumcenter.