MathDB

7

Part of 2010 Malaysia National Olympiad

Problems(3)

OMK 2010

Source:

6/4/2011
Let ABCABC be a triangle in which AB=ACAB=AC. A point II lies inside the triangle such that ∠ABI=∠CBI\angle ABI=\angle CBI and ∠BAI=∠CAI\angle BAI=\angle CAI. Prove that ∠BIA=90o+∠C2\angle BIA=90^o+\dfrac{\angle C}{2}
geometryincenter
OMK 2010

Source: Malaysia National Olympiad 2010 Muda Category Problem 7

6/4/2011
Let ABCABC be a triangle in which AB=ACAB=AC and let II be its incenter. It is known that BC=AB+AIBC=AB+AI. Let DD be a point on line BABA extended beyond AA such that AD=AIAD=AI. Prove that DAICDAIC is a cyclic quadrilateral.
symmetrygeometrycircumcirclegeometry unsolved
OMK 2010

Source: Malaysia National Olympiad 2010 Sulung Category Problem 7

6/4/2011
A line segment of length 1 is given on the plane. Show that a line segment of length 2010\sqrt{2010} can be constructed using only a straightedge and a compass.
geometryperpendicular bisectorgeometry unsolved