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If arc PQR above is a semicircle, what is the length of diameter PR?
(1) a=4
(2) b=1
ANSWER: D (Either is sufficient)
I kind of get it, but would like a thorough, clear explanation from all you smarties out there. Thanks!!
(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
Hence, answer is D...
Cheers...
You never win the Silver, you lose the Gold!!!!
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