Infinite Stack of Inscribed Circles in an Isosceles Triangle

If you inscribe a circle inside this 13-13-10 isosceles triangle, then construct a circle that is tangent to the first circle and the two legs of the isosceles triangle, then repeat that construction to create an infinite stack of circles inside the triangle? What is the sum of the circumferences of the infinite stack of circles inside the triangle?  What is the sum of the areas of the infinite stack of circles inside the triangle?
Problem supplied by CarolynGardner-Thomas at the Boston Math Teachers' Circle, October 2018.