MathDB

triangle construction given 3 points (Kyiv City Olympiad 2004 9.7)

Source:

June 27, 2021

geometryconstruction

Problem Statement

The board depicts the triangle

ABC

, the altitude

AH

and the angle bisector

AL

which intersectthe inscribed circle in the triangle at the points

M

and

N, P

and

Q

, respectively. After that, the figure was erased, leaving only the points

H, M

and

Q

. Restore the triangle

ABC

.
(Bogdan Rublev)