# Thread: Another one I need help on.

1. ## Another one I need help on.

The attached JPEG corresponds to this question.

If arc PQR above is a semicircle, what is the length of diameter PR?
(1) a=4
(2) b=1

I kind of get it, but would like a thorough, clear explanation from all you smarties out there. Thanks!!   Reply With Quote

2. ## Re: Another one I need help on.  Reply With Quote

3. ## Re: Another one I need help on.

(pls draw a figure on your end as I can't draw a figure here )

Let's say the centre of the circle is O and point where perpendicular from Q meets the diameter is M (so that QM = 2 as given in the figure)

Construct a line connecting centre O and Q, which will equal to the radius of the circle = r.

Statement - 1 : a = 4

In triangle QOM, applying pythagoras,
OQ^2 = MO^2+MQ^2
Here, OQ = r
MQ = 2
and MO = 4-r

Therefore, r^2 = (4-r)^2 + 2^2.... solving it gives you r = 2.5
So I is SUFFICIENT
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In a similar fashion, b = 1 gives you following equation,
r^2 = (r-1)^2 + 4.... solving it gives you r = 2.5
So II is SUFFICIENT

Cheers...  Reply With Quote