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Question
The figure given below, shows a circle with centre O. Given : ∠AOC = a and ∠ABC = b.
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Find the relationship between a and b.
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Find the measure of angle OAB, if OABC is a parallelogram.
Solution
i. ∠ABC = `1/2` Reflex (∠COA)
(Angle at the centre is double the angle at the circumference subtended by the same chord)
`=> b = 1/2 (360 - a)`
`=>` a + 2b = 360°
ii. Since OABC is a parallelogram, so opposite angles are equal.
2b + b = 360°
3b = 360°
b = 120°
∴ 120° + 120° + x + x = 360°
2x = 360° – 240°
2x = 120°
`x = (120^circ)/2`
x = 60°
`=>` ∠OAB = 60°
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