MathDB

2

Part of 1985 Vietnam Team Selection Test

Problems(2)

The locus of the incenter of triangle SBC

Source: Vietnam TST 1985 Problem 2

2/5/2010
Let ABC ABC be a triangle with AB \equal{} AC. A ray Ax Ax is constructed in space such that the three planar angles of the trihedral angle ABCx ABCx at its vertex A A are equal. If a point S S moves on Ax Ax, find the locus of the incenter of triangle SBC SBC.
geometryincenterperpendicular bisectorgeometry proposed
The equation has an odd number of solutions

Source: Vietnam TST 1985 Problem 5

2/5/2010
Find all real values of a for which the equation (a \minus{} 3x^2 \plus{} \cos \frac {9\pi x}{2})\sqrt {3 \minus{} ax} \equal{} 0 has an odd number of solutions in the interval [ \minus{} 1,5]
trigonometryfunctionalgebra proposedalgebra