You can use the pythagorean theorem to solve for the distance to the horizon. Any segment drawn from a point of tangency to the center is always perpendicular. Therefore, connect the segment from the point of tangency to the center, this is also a radius. Now, there is formed a right triangle in which one leg is the segment from point of tangency to center = 6371 km and the hypotenuse which is 6724 km (6371+353).
Use pythagoream theorem to find the horizon (leg) x.
`x^2 + 6371^2 = 6724^2`
` ` `x^2 = 4622535`
`x = 2150.00814` km