Question
Download Solution PDFIn the given figure, O is the centre of the circle and ∠AOC = 140°. Find ∠ABC.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven :
O is the centre of the circle
∠AOC =140°
Calculation:
O is the centre of the circle
Take a point D in remaining arc
∠AOC = 140°
∠AOC = 2∠ADC ( Angle formed by chord at centre = twice angle formed in same arc segment)
⇒ 140° = 2∠ADC
⇒ ∠ADC = 70°
ABCD will be a cyclic quadrilateral
Sum of opposite angles of cyclic quadrilateral = 180°
⇒ ∠ABC + ∠ADC= 180°
⇒ 70° + ∠ABC = 180°
⇒ ∠ABC = 110°
∴ Option 2 is the correct answer.
Last updated on Jul 12, 2025
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