A place I would like to share some concepts, ideas, puzzles that simulate the minds of those interested in Math - for competitions or fun.
Thursday, December 15, 2011
Puzzle 15 - Circle Square
Find the ordered pair (p, q) of rational numbers so that the radius of circle that passes through vertex D of square ABCD, and is tangent to sides AB and BC can be expressed as . Given that the side length of the square is equal to 1
Let O is the center and r is the radius of the circle. Let E, F are the points of contact of the circle with sides AB and BC respectively. If P is perpendicular dropped from O to the side AD, then we have from the right triangle OPD, OP=PO=1-r and OD=r. Hence r=2-sqrt(2). So, p=2, q=-1
. Given that the side length of the square is equal to 1
2 comments:
(2,-1).. thankyou sir for reminding sirkills and cood geometry 4m dasgupta book
Let O is the center and r is the radius of the circle. Let E, F are the points of contact of the circle with sides AB and BC respectively. If P is perpendicular dropped from O to the side AD, then we have from the right triangle OPD, OP=PO=1-r and OD=r. Hence r=2-sqrt(2). So, p=2, q=-1
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