CAT 2017 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Geometry Questions | Question 18

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Question 18 : ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120° and ∠BAC = 30°, then the value of ∠BCD (in degrees) is [TITA]


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Explanatory Answer

Method of solving this CAT Question from Geometry
CAT 2017 Question Paper Quants Slot 2 Geometry

ABCD is a quadrilateral inscribed in a circle with centre O.
∠COD = 120°
∠BAC = 30°
∠BOC = 60° (twice that of ∠BAC)
BOD is a straight line (60 + 120) = 180° or BD is the diameter of the circle
∠BOD = 180°
We have to find the value of ∠BCD
∠BCD is an angle in a semicircle = 90°

The question is "ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120° and ∠BAC = 30°, then the value of ∠BCD (in degrees) is [TITA]"

Hence, the answer is 90

 

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