A cyclic quadrilateral ABCD is such that AB = BC, AD = DC,

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A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC ⊥ BD, ∠CAD = θ. Then the angle ∠ABC =

1. θ
2. θ/2
3. 2θ
4. 3θ

Correct Option: C

On the basis of question we draw a figure of cyclic quadrilateral ABCD,

∠B + ∠D = 180° and ∠A + ∠C = 180°
⇒ ∠BAC = ∠BCA
∠DAC = ∠DCA
∴ ∠DAB = ∠DCB = 90° , ∠DAC = θ
∴ ∠ADE = 90° – θ = ∠CDE
∴ ∠ABC = 180° – 2(90° – θ)
∠ABC = 180° – 180° + 2θ = 2θ