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Tangent and Area Puzzle (Posted on 2015-08-01) Difficulty: 3 of 5
Two intersecting circles C1 and C2 have a common tangent which touches C1 at S and C2 at T. The two circles intersect at X and Y, where Y is nearer to ST than X is.

Determine (with proof) the ratio:
Area(Triangle XYS)/Area(Triangle XYT)

No Solution Yet Submitted by K Sengupta    
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Solution Comment 1 of 1

The line XY intersects the common tangent ST
at its midpoint M.
Let U and V be the perpendicular projections
of S and T onto line XY.
The right triangles SUM and TVM are congruent.
[XYS] = Area(triangle XYS) = |XY||SU|
[XYT] = Area(triangle XYT) = |XY||TV|
Therefore, [XYS]/[XYT] = 1

  Posted by Bractals on 2015-08-01 11:17:35
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