Why the three-point line flattens in the corners
Court markings
Where the arc is measured from, why it turns into a straight line near the sidelines, and what that does to where players stand.
The three-point arc is measured from a point directly under the centre of the rim, not from the backboard and not from the baseline. In the US professional game it sits 23 feet 9 inches away at the top. If you continued that radius all the way round, the arc would run off the side of the floor, because the court is 50 feet wide and the rim sits in the middle of it. So the line stops curving and becomes a straight segment parallel to each sideline, 22 feet from the basket.
That gives you a corner three that is nearly two feet shorter than one from the top of the key. Two feet does not sound like much until you watch a possession unfold. The same shot, worth the same three points, is simply easier from the corner, and every offence in the sport is built partly around putting someone there.
The geometry has a second effect that matters more. A player in the corner is in the furthest spot on the floor from the ball when the ball is on the opposite wing. His defender has the longest distance to cover if he helps on a drive and then has to recover. Coaches talk about the corner as a spacing position for exactly this reason: standing still in the right place pulls a defender out of the lane without anyone touching him.
The flattening is also why corner shooters stand so close to the sideline that it looks uncomfortable. The boundary sits three feet outside the line. Step back for balance and your heel is out of bounds, which is a turnover with no shot at all. Watch the feet of a shooter catching in the corner: good ones set them before the pass arrives and never adjust backwards.
International and US college courts use a slightly shorter radius, a little over 22 feet, and flatten in the corners for the same geometric reason, though the gap between corner and top is smaller. When a player moves between competitions, the corner is the shot that travels best, because the difference is measured in inches rather than feet.
Next time a possession resets, find the two corners first. If both are occupied and the ball is at the top, the defence has three defenders to guard four scoring threats in the middle of the floor, and that imbalance is the whole point of the line being shaped the way it is.