Given an acute-triangle ∆ ABC . From the vertices A ,B ,C draw perpendicular lines to the opposite sides of the triangle and let D ,E ,Z the feet of the perpendicular lines on the sides BC , AC, AB respectively. Let H be the point of intersection of the triangle's altitudes AD, BE, CZ .
I was able to solve the first questions using the midpoint theorem
Any help is considerable even,
- If Y ,K ,L ,I are the midpoints of the line segments AH , CH ,BC ,AB respectively, then prove that the quadrilateral YKLI is a rectangle
- Draw the tangent (ε) to the circle ,passing through the vertices of the rectangle YKLI, at the point Y. Prove that (ε) is parallel to the line ZΕΙ
I was able to solve the first questions using the midpoint theorem
Any help is considerable even,
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