I recently went on a bike ride where I noticed curiously that the start point, the finish point and the rest point were all exactly the same distance from my house.

The first leg of the ride involved riding 23 miles due east and then 7 miles due north, whereupon I arrived at the rest point.

The second leg of the ride involved riding 15 miles due east and then 9 miles due north to the finish.

How far is my house from the start/rest/finish points?