MathDB

Let

ABC

be a triangle, and

C^{\prime}

and

A^{\prime}

the midpoints of its sides

AB

and

BC

. Consider two lines

g

and

g^{\prime}

which both pass through the vertex

A

and are symmetric to each other with respect to the angle bisector of the angle

CAB

. Further, let

Y

and

Y^{\prime}

be the orthogonal projections of the point

B

on these lines

g

and

g^{\prime}

. Show that the points

Y

and

Y^{\prime}

are symmetric to each other with respect to the line

C^{\prime}A^{\prime}

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