One-seventh area triangle

In plane geometry, a triangle ABC contains a triangle having one-seventh of the area of ABC, which is formed as follows: the sides of this triangle lie on cevians p, q, r where p connects A to a point on BC that is one-third the distance from B to C, q connects B to a point on CA that is one-third the distance from C to A, r connects C to a point on AB that is one-third the distance from A to B. The proof of the existence of the one-seventh area triangle follows from the construction of six parallel lines: two parallel to p, one through C, the other through q.r two parallel to q, one through A, the other through r.p two parallel to r, one through B, the other through p.q. The suggestion of Hugo Steinhaus is that the (central) triangle with sides p,q,r be reflected in its sides and vertices.

Source: Wikipedia — One-seventh area triangle (CC BY-SA 4.0)

One-seventh area triangle

In plane geometry, a triangle ABC contains a triangle having one-seventh of the area of ABC, which is formed as follows: the sides of this triangle lie on cevians p, q, r where p connects A to a point on BC that is one-third the distance from B to C, q connects B to a point on CA that is one-third the distance from C to A, r connects C to a point on AB that is one-third the distance from A to B. The proof of the existence of the one-seventh area triangle follows from the construction of six parallel lines: two parallel to p, one through C, the other through q.r two parallel to q, one through A, the other through r.p two parallel to r, one through B, the other through p.q. The suggestion of Hugo Steinhaus is that the (central) triangle with sides p,q,r be reflected in its sides and vertices.

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Source: Wikipedia "One-seventh area triangle" · CC BY-SA 4.0

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