MathDB

AC = AA_1 if <ABC = 45^o, AA_1= _|_ CC_1 (2016 Kyiv City MO 9.5)

Source:

September 5, 2020

geometryequal segmentsperpendicularity

Problem Statement

On the sides

BC

and

AB

of the triangle

ABC

the points

{{A} _ {1}}

and

{{C} _ {1}}

are selected accordingly so that the segments

A {{A} _ {1}}

and

C {{C} _ {1}}

are equal and perpendicular. Prove that if

\angle ABC = 45 {} ^ \circ

, then

AC = A {{A} _ {1}}

.
(Gogolev Andrew)