Answer:
NF = 16 units
Explanation:
- The in-center of a triangle is a point inside the triangle and equidistant from the three sides of the triangle
- It is the center of the circle which touch the three sides of the triangle (each side of a triangle is tangent to the circle and the segments drawn from it to the points of tangent are radii of the circle)
∵ N is the in-center of ΔABC
∴ N is equidistant from the sides AB, BC and CA
- That means the perpendicular segments from N to AB, BC
and AC are equal
∴ ND = NE = NF
∵ ND = 6x - 2
∵ NE = 3x + 7
- Equate them to find x
∴ 6x - 2 = 3x + 7
- Subtract 3x from both sides
∴ 3x - 2 = 7
- Add 2 to both sides
∴ 3x = 9
- Divide both sides by 3
∴ x = 3
- Substitute the value of x in ND to find its length
∵ ND = 6(3) - 2 = 18 - 2
∴ ND = 16 units
∵ ND = NE = NF
∴ NF = 16 units