MathDB

triangle by symmetric points, area, construction (2003 Romania District VII P4)

Source:

May 24, 2020

geometryconstructionarea of a triangleSymmetric

Problem Statement

Let

ABC

be a triangle. Let

B'

be the symmetric of

B

with respect to

C, C'

the symmetry of

C

with respect to

A

and

A'

the symmetry of

A

with respect to

B

.
a) Prove that the area of triangle

AC'A'

is twice the area of triangle

ABC

. b) If we delete points

A, B, C

, how can they be reconstituted? Justify your reasoning.