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Question

C is a point on the minor arc AB of the circle, with the centre O. Given   ACB = x and  AOB =  y .Express y in terms of x. Calculate x, if ACBO is a parallelogarm.


Solution

Clearly, major arc BA subtends x at a point on the remaining part of the circle.

image

Reflex AOB = 2x
360 - y = 2x
y = 360 - 2x

Since ACBO is a parallelogram.

 x = y   i.e.  x = y
x = 360 -2x
3x = 360
x = 120

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