MathDB

4

Part of 1968 Dutch Mathematical Olympiad

Problems(1)

line construction, which coincides with itself after reflections wrt 3 lines

Source: Netherlands - Dutch NMO 1968 p4

2/1/2023
Given is a triangle ABCABC. A line ℓ\ell passes through reflection wrt BCBC changes into the line ℓ′\ell', ℓ′\ell' changes into ℓ′′\ell'' through reflection wrt ACAC and ℓ′′\ell'' through reflection wrt ABAB changes into ℓ′′′\ell'''. Construct the line ℓ\ell given that ℓ′′′\ell''' coincides with ℓ\ell.
geometryreflectionconstruction