MathDB

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

S_1 , S_2

and

S_3

, the three sector-like regions with vertices at

A, B

and

C

(as in the diagram). Find the value of

S_1 +S_2 +S_3 -S

." Prove that each student would obtain the same result . https://1.bp.blogspot.com/-K3kHWWWgxgU/XWHRQ8WqqPI/AAAAAAAAKjE/0iO4-Yz6p9AcM2mklprX_M18xTyg9O81gCK4BGAYYCw/s200/TOT%2B1985%2BAutumn%2BJ3.png ( A . K . Tolpygo, Kiev)

Problem Statement