MathDB

1

Part of 1998 China National Olympiad

Problems(2)

Find sin A if sqrt(2) OI = AB - AC

Source: Chinese Mathematical Olympiad 1998 Problem 1

8/22/2013
Let ABCABC be a non-obtuse triangle satisfying AB>ACAB>AC and ∠B=45∘\angle B=45^{\circ}. The circumcentre OO and incentre II of triangle ABCABC are such that 2 OI=AB−AC\sqrt{2}\ OI=AB-AC. Find the value of sin⁡A\sin A.
geometryincentertrigonometrygeometry unsolved
Divisible by 2^2000

Source: Chinese Mathematical Olympiad 1998 Problem 4

8/22/2013
Find all natural numbers n>3n>3, such that 220002^{2000} is divisible by 1+Cn1+Cn2+Cn31+C^1_n+C^2_n+C^3_n.
number theory unsolvednumber theory