MathDB

2

Part of 2002 Poland - Second Round

Problems(2)

Right triangle ABC is base of pyramid ABCD, AD=BD and AB=CD

Source:

2/2/2011
Triangle ABCABC with ∠BAC=90∘\angle BAC=90^{\circ} is the base of the pyramid ABCDABCD. Moreover, AD=BDAD=BD and AB=CDAB=CD. Prove that ∠ACD≥30∘\angle ACD\ge 30^{\circ}.
geometry3D geometrypyramidgeometry proposed
Quadraliteral with strange angles

Source:

1/6/2008
In a convex quadrilateral ABCDABCD, both ∠ADB=2∠ACB\angle ADB=2\angle ACB and ∠BDC=2∠BAC\angle BDC=2\angle BAC. Prove that AD=CDAD=CD.
geometrycircumcirclegeometry unsolved