MathDB

9.3

Part of III Soros Olympiad 1996 - 97 (Russia)

Problems(3)

sets of projections of a square on lines (III Soros Olympiad 1996-97 R1 9.3)

Source:

5/29/2024
Draw the set of projections of a square given on a plane onto all possible lines passing through a given point OO of the plane lying outside the square.
geometry
compurational geo with 2 circumcircles and angle bisector

Source: III Soros Olympiad 1996-97 R2 9.3 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

5/31/2024
In triangle ABCABC, sides CBCB and CACA are equal to aa and bb, respectively. The bisector of the angle ACBACB intersects the side ABAB at the point KK and the circumscribed circle of the triangle at point MM. The circumscribed circle of the triangle AMKAMK intersects for second time the straight line CACA at the point PP. Find the length of the segment APAP.
geometryangle bisector
computational 3D geo , ABCD (III Soros Olympiad 1996-97 R3 9.3)

Source:

5/31/2024
Let ABCDABCD be a three-link broken line in space, all links of which are equal and ∠BCD=90o\angle BCD=90^o. Find the distance from AA to the midpoint of BDBD, if AD=aAD = a.



geometry3D geometry