MathDB

1

Part of 1997 Turkey Team Selection Test

Problems(2)

Turkey TST 1997 Problem 1, sum of inradii

Source: Turkey TST 1997 Problem 1

11/30/2011
In a triangle ABCABC with a right angle at AA, HH is the foot of the altitude from AA. Prove that the sum of the inradii of the triangles ABCABC, ABHABH, and AHCAHC is equal to AHAH.
geometryinradiusincenterarea of a trianglegeometry proposed
Turkey TST 1997 Problem 4, compute AC+CE

Source: Turkey TST 1997 Problem 4

11/30/2011
A convex ABCDEABCDE is inscribed in a unit circle, AEAE being its diameter. If AB=aAB = a, BC=bBC = b, CD=cCD = c, DE=dDE = d and ab=cd=14ab = cd =\frac{1}{4}, compute AC+CEAC + CE in terms of a,b,c,d.a, b, c, d.
trigonometrygeometry proposedgeometry