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Circle and Square Tryst Again

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by dtweah » Tue May 12, 2009 12:12 pm
A circle passes through two adjacent vertices A,B of a square and is tangent to the side opposite the side having endpoints A and B. If the sides of the square have length 8 then the radius of the circle is

(a) 19/4
(b) 4
(c) 5
(d) 9/2
d) 16/Pi
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Re: Circle and Square Tryst Again

by kanha81 » Tue May 12, 2009 1:34 pm
dtweah wrote:A circle passes through two adjacent vertices A,B of a square and is tangent to the side opposite the side having endpoints A and B. If the sides of the square have length 8 then the radius of the circle is

(a) 19/4
(b) 4
(c) 5
(d) 9/2
d) 16/Pi
[spoiler][C][/spoiler]

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Re: Circle and Square Tryst Again

by dtweah » Wed May 13, 2009 2:01 am
kanha81 wrote:
dtweah wrote:A circle passes through two adjacent vertices A,B of a square and is tangent to the side opposite the side having endpoints A and B. If the sides of the square have length 8 then the radius of the circle is

(a) 19/4
(b) 4
(c) 5
(d) 9/2
d) 16/Pi
[spoiler][C][/spoiler]

Check the attachment

(c) Let O be the center of the circle, M the midpoint of the side AB, and T the point of tangency on the opposite side of the square. Then O is on the line MT since OM and OT are perpendicular to parallel sides of the square. Thus the right triangle OMA has hypotenuse r and sides 8 – r and 4. Therefore r2 = 42 + (8 – r)2 from which r = 5.
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