MathDB

2

Part of 1992 Cono Sur Olympiad

Problems(2)

Find two points

Source: Cono Sur 1992-problem 2

5/29/2006
Let PP be a point outside the circle CC. Find two points QQ and RR on the circle, such that P,QP,Q and RR are collinear and QQ is the midpopint of the segmenet PRPR. (Discuss the number of solutions).
geometry unsolvedgeometry
Proof in a triangle

Source: Cono Sur 1992-problem 5

5/29/2006
In a △ABC\triangle {ABC}, consider a point EE in BCBC such that AE⊥BCAE \perp BC. Prove that AE=bc2rAE=\frac{bc}{2r}, where rr is the radio of the circle circumscripte, b=ACb=AC and c=ABc=AB.
trigonometrygeometrycircumcirclegeometry unsolved