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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.

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