A cyclic quadrilateral ABCD is such that AB = BC, AD = DC, AC \perp BD , \angleCAD = \theta . Then the angle ∠ABC =

RRB Junior Engineer Stage 1 Model Papers 2

Question : 14 of 99

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

AC ⊥ BD

∠CAD = θ

. Then the angle ∠ABC =

Solution:

∠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

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