Check the picture below.
so, two tangents to the same circle, whenever they meet outside the circle, they'll be congruent, namely, AB = AX and CB = CY and DX = DY.
well, we know AB = BC, and we know that AB = AX and CB = CY, therefore
AB = BC = AX = CY = 10.
an isosceles needs twin sides, well, we know DX = DY, and we know that AX = 10 then the triangle's side AD = AX + DX = 10 + DX.
the triangle's side of CD = CY + DY = 10 + DY.
but but but, we know DX and DY are tangents to a common circle meeting outside, so they're equal, so whatever length DX and DY are, is the same, so
10 + DY = 10 + DX
meaning the triangle's sides AX = CD, and for an isosceles, is all you need, twin sides.
