MathDB

2021 Sharygin Geometry Olympiad

Part of Sharygin Geometry Olympiad

Subcontests

(48)
10-11.8
1
10-11.7
1
10-11.6
1
10-11.5
1
9.8
1
9.7
1

2 player game of drawing altitudes, one draws, other erases points

Three sidelines of on acute-angled triangle are drawn on the plane. Fyodor wants to draw the altitudes of this triangle using a ruler and a compass. Ivan obstructs him using an eraser. For each move Fyodor may draw one line through two markeed points or one circle centered at a marked point and passing through another marked point. After this Fyodor may mark an arbitrary number of points (the common points of drawn lines, arbitrary points on the drawn lines or arbitrary points on the plane). For each move Ivan erases at most three of marked point. (Fyodor may not use the erased points in his constructions but he may mark them for the second time). They move by turns, Fydors begins. Initially no points are marked. Can Fyodor draw the altitudes?
9.6
1
9.5
1
8.8
1
8.7
1
8.6
1
8.5
1
10-11.3
1
10-11.4
1
10-11.2
1
10-11.1
1
9.4
1
9.3
1
9.2
1
9.1
1
8.4
1
8.3
1
8.2
1
8.1
1
7
1
20
1
17
1
24
1
14
1
13
1
12
1
9
1
22
1
8
1
10
1
18
1
19
1
6
1
11
1
21
1
23
1
16
1
5
1
15
1
4
1
3
1
2
1
1
1