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O is the centre of a circle of radius 10 cm. P is any point in the circle such that OP = 6 cm.

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O is the centre of a circle of radius 10 cm. P is any point in the circle such that OP = 6 cm. A is the point travelling along the circumference. x is the distance from A to P. what are the least and the greatest values of x in cm? what is the position of the points O, P and A at these values?

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The least value of x will be when A is on OP produced, i.e. O, P and A are collinear.

∴ AP = OA - OP = 10 - 6 = 4 cm.

The maximum value of x will be when A is on PO produced, i.e. A, O and P are collinear.

∴ AP = OA + OP = 10 + 6 = 16 cm.

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