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CAT 2017 Slot 2 QA Question & Solution

GeometryMedium

Question

ABCD is a quadrilateral inscribed in a circle with centre O such that O lies inside the quadrilateral. If $\angle COD = 120$ degrees and $\angle BAC = 30$ degrees, then the value of $\angle BCD$ (in degrees) is

Solution

$\angle COD = 120$ => $\angle CAD = 120/2 = 60$ (The angle subtended by the chord DC at the major arc is half the angle subtended at the centre of the circle.)
$\angle BAC = 30$
$\angle BAD = \angle BAC + \angle CAD$ = 30 + 60 = 90
$\angle BCD = 180 - \angle BAD$ = 180 - 90 = 90