2
Problems(2)
max triangle area, starting with intersecting circles
Source: 2007 Oral Moscow Geometry Olympiad grades 10-11 p2
10/19/2020
Two circles intersect at points and . Point lies on the first circle, but outside the second. Lines and intersect the second circle at points and , respectively. Indicate the position of point at which triangle has the largest area.(D. Prokopenko)
geometrycirclesarea of trianglemax
EF = FL. wanted, starting with isosceles right triangle, BK=CL
Source: 2007 Oral Moscow Geometry Olympiad grades 8-9 p2
10/18/2020
An isosceles right-angled triangle is given. On the extensions of sides and , behind vertices and equal segments and were laid. and F are the points of intersection of the segment and the lines perpendicular to the , passing through the points and , respectively. Prove that .
geometryequal segmentsright triangleisosceles