A geometry problem by sri lakshmi topella
Geometry
Level
2
The area of triangle with vertices at the point is:
ab+bc+ca
0
a+b+c
none of these
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1 solution
The three points are collinear:
( b , c + a ) − ( a , b + c ) = ( b − a , a − b ) ⇒ ( a , b + c ) + 1 ⋅ ( b − a , a − b ) = ( b , c + a ) ;
( a , b + c ) + b − a c − a ⋅ ( b − a , a − b ) = ( c , a + b ) .
Therefore, the three points form a degenerate triangle and its area is 0. If a =b, the result is clear.