2012/2/1 Alexey Zaslavsky <

zasl@...>

> Let A_0, B_0, C_0 be the midpoints of sides BC, CA, AB; P be

> an arbitrary

> point on the Euler line of triangle ABC and A_1, B_1, C_1 be the

> projections

> of circumcenter O to AP, BP, CP. Then A_0A_1, B_0B_1, C_0C_1 concur.

Is this true as well?

Let ABC be a triangle AoBoCo the medial triangle, P a point

on the Euler line and A1,B1,C1 the orth. projections of O on

PAo, PBo, PCo resp.

The triangles ABC, A1B1C1 are perspective (?).

Locus Problem:

Let P be a variable point. Which is the locus of P such that

ABC, A1B1C1 are perspective?

Is it Euler Line + Something_Else ?

APH