A cyclic quadrilateral ABCD is such that AB = BC, AD = DC and AC, BD intersect at O and BD is angle bisector of ∠B. If ∠CAD = 46°, then the measure of ∠AOB is equal to:
90°
Given -
A cyclic quadrilateral ABCD is such that AB = BC, AD = DC and AC and BD intersect at O and ∠CAD = 46°
Concept used -
ABCD is a cyclic quadrilateral,
∠A + ∠C = ∠B + ∠D = 180°
Solution -

AD = CD
∠CAD = ∠DCA = 46°
∠ADC = 180° - 92° = 88°
∠ABC = 180° - 88° = 92°
AB = BC
⇒ ∠BAC = ∠BCA = 88°/2 = 44°
BD is angle bisector of ∠B.
⇒ ∠ABO = 46°
⇒ ∠AOB = 180° - (46° + 44°) = 90°
∴ ∠AOB is 90°.
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