if b,h are given, and may simply be calculated. so i assume that are given, and you wish to find b and h.

write:

from we get:

, which is a quadratic in h.

the discriminant is

however, aren't "independent" they both depend on the radius of the circle, r:

so , therefore: no real solutions for h.

however, in reviewing your original equations, it appears that your formula for either the area or the perimeter of the isoceles triangle is incorrect, if h is the height, then the perimeter length should be:

.

you might want to review that, and confirm (the calcuations get a lot messier if this is true).