Question

Two chords AB and AC of a circle subtends angles equal to 90º and 150º, respectively
at the centre. Find BAC, if AB and AC lie on the opposite sides of the centre

Answer 1


As the sum of all angles at a point = 360°
Hence ∠AOC+∠AOB+∠COB =360°
∴∠COB=360°−(∠AOC+∠AOB) =360°−(150°+90°) =360°−240°=120°Now consider the arc CB The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.Hence ∠COB = 2∠CAB⇒∠CAB =∠COB2=120°2=60° 

Answer 2

hope the above pic helps you