Question

What value of n would make point A the circumcenter?

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

Answer 1

Option 2 is true

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=(6)/(2)=3`

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

Answer 2

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

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.