MathDB

2

Part of 2007 South East Mathematical Olympiad

Problems(2)

semicircle problem

Source: China south east mathematical Olympiad 2007 problem 2

7/12/2013
ABAB is the diameter of semicircle OO. CC,DD are two arbitrary points on semicircle OO. Point PP lies on line CDCD such that line PBPB is tangent to semicircle OO at BB. Line POPO intersects line CACA, ADAD at point EE, FF respectively. Prove that OEOE=OFOF.
geometrygeometric transformationreflectionparallelogramgeometry unsolved
right-angle triangle ABC

Source: China south east mathematical Olympiad 2007 problem 6

7/12/2013
In right-angle triangle ABCABC, ∠C=90\angle C=90°, Point DD is the midpoint of side ABAB. Points MM and CC lie on the same side of ABAB such that MB⊥ABMB\bot AB, line MDMD intersects side ACAC at NN, line MCMC intersects side ABAB at EE. Show that ∠DBN=∠BCE\angle DBN=\angle BCE.
geometrycircumcirclecyclic quadrilateralgeometry unsolved