A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC is perpendicular to BD and ∠CAD = θ, then find the ∠ABC. A. θ B. θ/2 C. 2θ D. 3θ

A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC is perpendicular to BD and ∠CAD = θ, then find the ∠ABC.

1. θ
2. θ/2
3. 2θ
4. 3θ

Answer & Explanation

Answer: Option C
∠B + ∠D = 180°
∠A + ∠C = 180°
∠BAC = ∠BCA ∠DAC = ∠DCA
∴∠DAB = ∠DCB = 90°
∠DAC = θ
∴∠ADE = 90° - θ = ∠CDE
∴ ∠ABC = 180° – 2(90° - θ) = 2θ

TAGS:

A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC is perpendicular to BD and ∠CAD = θ, then find the ∠ABC. A. θ B. θ/2 C. 2θ D. 3θA cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC is perpendicular to BD and ∠CAD = θ, then find the ∠ABC. A. θ B. θ/2 C. 2θ D. 3θA cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC is perpendicular to BD and ∠CAD = θ, then find the ∠ABC. A. θ B. θ/2 C. 2θ D. 3θ