Question

A total solar eclipse occurs when the moon passes
between the earth and the sun, and the darkest
shadow cast by the moon, called the umbra, hits the surface of the earth. If the umbra does not hit the surface, as shown in the following figure, then a total solar eclipse is not possible. In other words, for a total solar eclipse to occur, point P must lie inside the circle for the earth.Assume the diameter of the sun is 870,000 miles, the diameter of the moon is 2160 miles, the diameter of the earth is 7920 miles, and the distance from the center of the sun to the center of the earth is approximately 93,000,000 miles. The distance from the moon to the earth varies, but the maximum distance from the center of the moon to the center of the earth is 252,700 miles, and is called the lunar apogee. How far is P from the center of the earth during lunar apogee?