Rectangle with unit circles
ABCD is a rectangle with AB=5. 2 circles of radius 1 are constructed inside the rectangle, one tangent to segments AB and AD, and the other tangent to BC and CD. Segment AC intersects the 2 circles at W, X, Y, Z in that order when going across the line. If WZ=23/Sqrt(5), then find BC.
The answer is 10.
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1 solution
CENTRE OF CIRCLE WX AS DIAMETER IS O1& CENTRE OF OTHER ONE IS O2. AC=WZ+AW+ZC=WZ+(02C-02Z)+(O1A-01W)=23/(5)^.5+2(2^.5-1) AB^2+BC^2=AC^2 GIVES BC =9.93=(approx)10