In ΔABC,
AB = AC (Given)
∴ ∠ACB = ∠ABC (Angles opposite to equal sides of a triangle are also equal)
In ΔACD,
AC = AD
∴ ∠ADC = ∠ACD (Angles opposite to equal sides of a triangle are also equal) In ΔBCD,
∠ABC + ∠BCD + ∠ADC = 180 (Angle sum property of a triangle)
∴ ∠ACB + ∠ACB +∠ACD + ∠ACD = 180
∴ 2(∠ACB + ∠ACD) = 180
∴ 2(∠BCD) = 180
∴ ∠BCD = 90