Its another side now

Geometry Level 5

The figure shows a square A B C D ABCD of side 6. It contains arcs B D BD and A C AC drawn with centers at A A and D D , respectively. If x x is the radius of the circle tangent to A B AB and arcs A C AC and B D BD . What is the value of x x ?


The answer is 1.000.

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1 solution

Nibedan Mukherjee
Jul 16, 2016

3 Helpful 0 Interesting 1 Brilliant 0 Confused

Let FA = y, EA = 6-x, FE = x => (6-x)^2 = x^2 + y^2. Draw a line from F across length of square to other side and let it be H: EH = 6-x, HD = FA = y, ED = 6+x => (6+x)^2 = (6-x)^2 + y^2. (6-x)^2 = x^2 + y^2. (6+x)^2 = (6-x)^2 + y^2. (6+x)^2 = (6-x)^2 + (6-x)^2 - x^2. 36 + 12x + x^2 = 36 - 12x + x^2 + 36 -12x + x^2 - x^2. 36 + 12x = 72 - 24x => 36x = 36 => x = 1.

E Koh - 4 months ago

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