1. on the verge of
on the verge of tears/success
Ben and Lucy’s marriage was so bad they were on the verge of divorce.
The team was excited and nervous beginning the day on the verge of the victory.
English word "on the brink of"(on the verge of) occurs in sets:
Sprawdzian angielski readingi pt. 22. on the point of
Have you heard they're on the point of starting an Underground Library.
I was on the point of cancelling the reservation.
3. a situation when you are almost in a new situation
4. at the point of experiencing or undergoing something often something significant or dangerous