The International Solar Terrestrial Physics database of the magnetic measurements on GOES and plasma measurements on Los Alamos National Laboratory (LANL) geosynchronous satellites is used for selection of 169 case events containing 638 geosynchronous magnetopause crossings (GMCs) in 1995 to 2001. The GMCs and magnetosheath intervals associated with them are identified using advanced methods that take into account (1) strong deviation of the magnetic field measured by GOES from the magnetospheric field, (2) high correlation between the GOES magnetic field and interplanetary magnetic field (IMF), and (3) substantial increase of the midenergy ion and electron fluxes measured by LANL. Accurate determination of the upstream solar wind conditions for the GMCs is performed using correlation of geomagnetic activity (Dst (SYM-H) index) with the upstream solar wind pressure. The location of the GMCs and associated upstream solar wind conditions are ordered in an aberrated GSM coordinate system (aGSM) with X-axis directed along the solar wind flow. In the selected data set of GMCs the solar wind total pressure Psw varies up to 100 nPa and the southward IMF Bz reaches 60 nT. We study the conditions necessary for geosynchronous magnetopause crossings using scatterplots of the GMCs in the coordinate space of Psw versus Bz. In such a representation the upstream solar wind conditions show a sharp envelope boundary beyond which no GMCs are observed. The boundary has two straight horizontal branches where Bz does not influence the magnetopause location. The first branch is located in the range of Psw = 21 nPa for large positive Bz and is associated with a regime of pressure balance. The second branch asymptotically approaches the range of Psw = 4.8 nPa under strong negative Bz, and it is associated with a regime in which the Bz influence saturates. The intermediate region of the boundary ranges from moderate negative to moderate positive IMF Bz and can be well approximated by a hyperbolic tangent function. We interpret the envelope boundary as a range of necessary upstream solar wind conditions required for the magnetopause to reach geosynchronous orbit at its closest approach to the Earth (its "perigee" location).