MathDB

collinear wanted, 3 similar trapezoids related 2016-17 D&uuml;rer Round1 D4 D+2

Source:

December 9, 2022

geometrytrapezoidDurercollinear

Problem Statement

Let the trapezoids

A_iB_iC_iD_i

(

i = 1, 2, 3

) be similar and have the same clockwise direction. Their angles at

A_i

and

B_i

are

60^o

and the sides

A_1B_1

B_2C_2

and

A_3D_3

are parallel. The lines

B_iD_{i+1}

and

C_iA_{i+1}

intersect at the point

P_i

(the indices are understood cyclically, i.e.

A_4 = A_1

and

D_4 = D_1

). Prove that the points

P_1

P_2

and

P_3

lie on a line.