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Problems(2)
angle bisector perpendicular to the median, twice in the same figure
Source: 2013 Oral Moscow Geometry Olympiad grades 8-9 p1
8/14/2019
In triangle the angle bisector is perpendicular on the median is . Prove that in the triangle also one of angle bisectors are perpendicular to one of the medians.
geometryangle bisectorperpendicularmedian
diagonal intersection of cyclic ABCD is incenter of BMC, circumcircles related
Source: 2013 Oral Moscow Geometry Olympiad grades 10-11 p1
8/16/2019
Diagonals of a cyclic quadrilateral intersect at point . The circumscribed circles of triangles and intersect at point on the side . Prove that the point is the center of the inscribed circle of the triangle .
geometryincentercircumcirclecyclic quadrilateral