ABCD is a quadrilateral with ∠ADC=∠ACD, ∠ACB=∠ABC and CD=7. If triangles ADC and ABC have perimeter 51 and 59, respectively, what is the value of BC?

Answer 1

It should be easy to see that
AB = AC = AD
let each one be x
in triangle ADC
2x + 7 = 51
2x= 44
x = 22

in triangle ABC
2x + BC = 59
44 + BC = 59
BC = 15