The heights AK and BL are drawn in triangle ABC. Prove that a circle can be circumscribed about ALKB.
| February 28, 2021 | education
Triangle ABL is rectangular, since BL is perpendicular to AC, so a circle can be described near it.
The center of the circle lies in the middle of the hypotenuse AB.
Triangle ABK is also rectangular since AK is perpendicular to BC.
Therefore, a circle can also be described near it, and the center of this circle is in the middle of the segment AB.
The centers of the circles coincide and the hypotenuses of the triangles are equal.
This means that the circles in the first and second cases coincide and points A, B, K, L belong to the same circle.
Therefore, a circle can be described around the quadrilateral ALKB.
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