Question

An isosceles triangle with height 10 and base 6 is inscribed in a circle find the diameter

Answer 1

A sketch of an isosceles triangle inscribed in a circle is shown in the attached figure.
From the information provided:
AM = 10
BC = 6
BM = MC = 1/2*6 = 3

Now,
tan a = BM/AM = 3/10 = 0.3
Then,
a = tan^-1(0.3) = 16.7°

Additionally,
2a = 2*16.7 = 33.4°

Therefore,
tan (2a) = BM/OM = 3/OM
OM = 3/[tan (2a)] = 3/tan 33.4 = 4.55

In this regard,
Radius = AO = AM-OM = 10-4.55 = 5.45