Howdy,
Your pears are leaking because they've been left to over rippen,
Pears like plums should be picked when firm, its the stem from the tree to the pear that the growers look at for signs of when to harvest the fruit,
IE the stem thickens and is a more brown than green colour,

the term your using "leaking" is termed weeping and its a sign your pear has over ripe.

We tend to eat fruit just at its peak of being mature after this point the fruits loose flavour and infact they are starting to rot,
your pear is bursting with juice and in a short while will rot.
If you leave fruit for to long on the tree you'll attract wasp and other insects.

That doesn't look like a ripe pear, it looks like one that's still growing. If that's correct, I can see evidence of something black at the top of the crack from which the sap is oozing. Cut some in half and see if there's an invader in there - because you're in the States, there's a wider range of pests that we don't get here, but Oriental Fruit Moth infestation springs to mind. If its that, there'll be a caterpillar inside the fruit, or at least evidence there has been one, and you may have the remains of cocoons on the branches in the tree, but you may have other local pests which can cause this.