CAT 2017 Slot 2 — QA Question 18
Basics of QuadrilateralsEasy
ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is
Answer & solution
Answer: 90
Solution
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Angle subtended by an arc on circle is half of the angle it makes at the center.
∴âââââââ Considering arc CD, it makes an angle of 120° at the center hence ∠CAD = 60°.
⇒ ∠BAD = 90°
Now, in a cyclic quadrilateral, sum of opposite angle = 90°.
⇒ ∠BAD + ∠BCD = 90°
∴ ∠BCD = 90°
Hence, 90.