MathDB

97

Part of 1985 IMO Longlists

Problems(1)

Show that there exists a point A

Source:

9/14/2010
In a plane a circle with radius RR and center ww and a line Λ\Lambda are given. The distance between ww and Λ\Lambda is d,d>Rd, d > R. The points MM and NN are chosen on Λ\Lambda in such a way that the circle with diameter MNMN is externally tangent to the given circle. Show that there exists a point AA in the plane such that all the segments MNMN are seen in a constant angle from A.A.
analytic geometrysymmetrytrigonometryfunctiongeometryperpendicular bisectorPythagorean Theorem