geometry question

Quote:

Originally Posted by requal

Hi I need help with this question(View the diagram attached!)

The diagram shows the point P on the rim of a circular wheel, centre O and of radius 2m. A 4.5m length of steel PA joins P to a point A which is free to move along the horizontal groove OQ, as the wheel rotates about its fixed centre O.

i) How far will A be from the centre of the circle when P is vertically above O? (the answer is $\frac{1}{2}\sqrt{65}m$ )
ii) What will be the closest that A comes to O?(the answer is $25m$ )
iii) What will be the furthest that A can be from O?(the answer is $6.5m$ )

I hope this reply doesn't come too late.

I've modified your sketch a little bit. Unfortunately I have messed up the order of questions.

to #i) Use Pythagorean theorem.

to #ii) Calculate a difference. (By the way: The given answer is wrong)

to #iii) Calculate a sum.