A teacher gives each student in the class the following task in their exercise book .
"Take two concentric circles of radius 1 and 10 . To the smaller circle produce three tangents whose intersections A,B and C lie in the larger circle . Measure the area S of triangle ABC, and areas S1,S2 and S3 , the three sector-like regions with vertices at A,B and C (as in the diagram). Find the value of S1+S2+S3−S."
Prove that each student would obtain the same result .
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( A . K . Tolpygo, Kiev) geometryconcentric circlescirclesTangentsareas