Given, AB = AC
Also, AB = AD hence, AD= AC
In the triangle ABC, angle B = angle ACB
In the triangle ACD, angle ACD = angle C - angle B
In the triangle ACD, angle D = angle ACD as AD = AC
=> angle C - angle B = angle D
=> angle C = angle B + angle D
since sum of angles B, C and D is 180 deg.
angle C = 90 and angle B + angle D = 90.
so angle BCD =90 deg.