## Maths Olympiad Questions | Maths Olympiad Question Papers | Maths Olympiad eBook

Posted by celebrityphotosnews on September 7, 2009

1. Let ABC be an acute angles triangle; AD be the bisector of angle BAC with D on BC; and BE be the altitude from B on AC. Show that angle CED > 45 degrees.

2. How Many 6-digit numbers are there such that :

(a) the digist of each number are all from the set {1,2,3,4,5};

(b) any digit that appears in the number appears at least twice ?

3. All the points in the plane are coloured using three colours. Prove that there exists a triangle with vertices having the smae colour that wither it is isosceles or its angles are in geometric progression.

4. Let ABC be a triangle and let P be an interior point sucg that angle BPC = 90 degrees, angle BAP = able BCP. Let M,N be the mid-points of AC, BC respectively. Suppose BP = 2PM. Prove that A,P, N are collinear.

Various Mathematical Olympiad questions and answers can be downloaded from the given links below : (copy paste the links in your browser)

http://www.samf.ac.za/samo/questions.html

http://olympiads.win.tue.nl/imo/

http://www.isid.ac.in/~rbb/rmoqpapers.html

http://www.imo-official.org/

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