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In this work we describe the method and results of precise solar astrometry made with the Michelson Doppler Imager (MDI), on board the Solar and Heliospheric Observatory (SOHO), during one complete solar cycle. We measured an upper limit to the solar radius variation, the absolute solar radius value and the solar shape. Our results are 22 mas peak-to-peak upper limit for the solar radius variation over the solar cycle, the absolute radius was measured as 959.28 ± 0.15 arcsec at 1 AU and the difference between polar and equatorial solar radii in 1997 was 5 km and about three times larger in 2001.