PR is a ‘personal record’, so in January I ran the fastest half marathon I have ever ran.
The tangents are the shortest path between two curves (geometry term). The course is measured by taking the shortest path possible - so inside of one corner to the inside of the next corner. If you ran down the middle of the road/path the whole race, you would be running farther than 13.1. It’s not very easy (or even really possible unless you are at the very front of the race) to run a perfect distance race. A little mileage will be added because of all the people, but by trying to stick as close to the tangents as possible and trying not to weave too much around people (wait/slow a little bit to see if a gap will open), you won’t add as much extra distance if you were not paying attention.