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collinear wanted, perpendiculars and altitudes related

Source: 2020 Indonedia MO Province P2 q4 OSP

December 11, 2020

geometrycollinearaltitudes

Problem Statement

It is known that triangle

B_A

is not isosceles with altitudes of

AA_1, BB_1

, and

CC_1

. Suppose

B_A

and

C_A

respectively points on

BB_1

and

CC_1

so that

A_1B_A

is perpendicular on

BB_1

and

A_1C_A

is perpendicular on

CC_1

. Lines

B_AC_A

and

BC

intersect at the point

T_A

. Define in the same way the points

T_C

and

T_C

. Prove that points

T_A, T_B

, and

T_C

are collinear.

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