Distance to the horizon

The Greatest distance occurs when the line connecting the satellites is tangential to the outline of the earth.

Consider the following Model

Given that this line will be Tangential, it will intersect the Circle at the point P, and the angle between the radius and this tangent shall be a right angle (by Circle Theorem) and P shall have a distance from C of 4000 as it lies on the circle.

This forms 2 distinct right triangles (CPS1 and CPS2) of which 2 lengths are known.

The triangle formed by Satellite 1 (S1), has a hypotenuse length of 4096 as S1 is 96 Miles above the surface of the earth.

Likewise, the triangle formed by Satellite 2 (S2), has a Hypotenuse of 4137 as S2 is 137 Miles above the surface of the earth. . Using Pythagoras' Theorem, we get PS1 being 881.6 and PS2 being 1055.82.

881.6 + 1055.82 = 1937.42.

Closest answer is 1900.

import math x = math.sqrt(8137 137) + math.sqrt(8096 96) print(x)

4096×(sin(cos⁻¹(4000÷4096))) + 4137×(sin(cos⁻¹(4000÷4137))) Just using trig instead of Pythagoras because it's too early in the morning.