how to solve for radius of horizontal curve with coordinates(NE) for points A,B, C on the curve

Answer 1

By horizontal curve, I suppose you mean an arc and not a spiral.

When three points A,B and C are given in order of chainage, you can find the radius first by finding the centre O, which in turn is at the intersection of any two diameters. You can find two diameters as the perpendicular bisectors of chords AB and BC.

Finally, the radius is the distance between O and A (or B, or C). Do check your calculations by finding the distances OA, OB and OC.

If you need help in finding the line along perpendicular bisector between two given points A(xa,ya) and B(xb,yb), here it is:
1. Find the line passing through AB.
2. calculate the slope the the preceding line, m.
3. find the mid-point D between A and B.
4. the perpendicular bisector is the line passing through D with a slope of -1/m.

Answer 2

kinda lost maybe help if gave more information,

Point A : N1405.4018
E1256.7569

Point B : N1283.3703
E1294.7027

Point C : N1225.9373
E1286.6137

Could please explain one more time, thank you