CAIRO (AP) — Egypt has rushed to try to broker a cease-fire deal between Israel and Hamas while also trying to prove itself to the Biden administration and the world as the main mediator in a conflict that threatens to worsen. It’s the latest instance in which Egypt has served as a mediator between Israel and Gaza’s ruling militant Hamas group. Egypt borders both Israel and the Gaza Strip, and has been a key player since Israel withdrew troops from Gaza in 2005 and Hamas seized the territory in 2007. But Egypt is also a walking a careful line with its own citizens, who deeply oppose Israel’s policies towards the Palestinians.