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Analytical Geometry

Blazing goIITian

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13 Jan 2009 19:24:53 IST

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The Rectangle at the Corner In the above figure, the rectangle at the corner measures 1 cm

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puzzle : Rectangle at the Corner

In the above figure, the rectangle at the corner measures 1 cm x 2 cm. What is the radius of the circle in cm?

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Comments (6)

Aatish Pandit

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13 Jan 2009 19:28:56 IST

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4 cm..

Jayant Dalmia

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25 Feb 2009 16:38:00 IST

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The answer is not 4 but 5cm. I've used the basic equation of the circle but i know there must be a non-coordinate way to solve it.

Aditya

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25 Feb 2009 16:48:57 IST

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pls do tell me the technique!

Yagyadutt Mishra

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25 Feb 2009 17:09:20 IST

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consider the two side of rectangles as the axis of co-ordinate system with left uppermost corner as origin.Then the circle looks like touching both the axis and passing through (2,1)...{point is clear or not plz rply}.

then equation can be written as,,

(x-a)^2 + (y-a)^2 = a^2.......{where a is the radius ...and (a,a) will be centre}

on solving we will have...x^2 + y^2 -2ax -2ay +a^2 = 0....put the point you will get quadratic in a and get two values.

a=5 and a=1.{which is neglected because breadth of rectangle has this dimension which is smaller than radius of circle}

Rahul Duggal

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25 Feb 2009 17:10:31 IST

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Correction: please ignore r is positive part

In second Last Line r can be 1 also but we know r>1 as side of rectangle is < radius

Yagyadutt Mishra

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25 Feb 2009 17:33:26 IST

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r is positive for the both case..from the equation..so i have suggested why we have to neglect it.

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