\PGset[0.8em]
\begin{picture}(10.5,10.5)

% In a given circle let AOB be a diameter, OC any radius, CD the
% perpendicular from C to AB.  Upon OC take OM equal to CD.  Find the
% locus of the point M as OC turns about O.

% r = 4.25
% Ellipse:  u = 5.25  v = 5.25  a = 4.25  b = 4.25  phi = 0.0 Grad
\qbezier(9.5, 5.25)(9.5, 7.0104)(8.2552, 8.2552)
\qbezier(8.2552, 8.2552)(7.0104, 9.5)(5.25, 9.5)
\qbezier(5.25, 9.5)(3.4896, 9.5)(2.2448, 8.2552)
\qbezier(2.2448, 8.2552)(1.0, 7.0104)(1.0, 5.25)
\qbezier(1.0, 5.25)(1.0, 3.4896)(2.2448, 2.2448)
\qbezier(2.2448, 2.2448)(3.4896, 1.0)(5.25, 1.0)
\qbezier(5.25, 1.0)(7.0104, 1.0)(8.2552, 2.2448)
\qbezier(8.2552, 2.2448)(9.5, 3.4896)(9.5, 5.25)

\drawline(1,5.25)(9.5,5.25) % BA
\dashline[80]{0.2}(5.25,1)(5.25,9.5) % EO
\drawline(5.25,5.25)(8.255,8.255)(8.255,5.25) % OCD

% Ellipse:  u = 5.25  v = 7.375  a = 2.125  b = 2.125  phi = 0.0 Grad
\qbezier[10](7.375, 7.375)(7.375, 8.2552)(6.7526, 8.8776)
\qbezier[10](6.7526, 8.8776)(6.1302, 9.5)(5.25, 9.5)
\qbezier[10](5.25, 9.5)(4.3698, 9.5)(3.7474, 8.8776)
\qbezier[10](3.7474, 8.8776)(3.125, 8.2552)(3.125, 7.375)
\qbezier[10](3.125, 7.375)(3.125, 6.4948)(3.7474, 5.8724)
\qbezier[10](3.7474, 5.8724)(4.3698, 5.25)(5.25, 5.25)
\qbezier[10](5.25, 5.25)(6.1302, 5.25)(6.7526, 5.8724)
\qbezier[10](6.7526, 5.8724)(7.375, 6.4948)(7.375, 7.375)

\dashline[80]{0.2}(5.25,9.5)(7.375,7.375) % EM

\put( 9.5, 5.0){$\scriptstyle A$}
\put( 0.2, 5.0){$\scriptstyle B$}
\put( 8.3, 8.3){$\scriptstyle C$}
\put( 7.8, 4.5){$\scriptstyle D$}
\put( 5.0, 9.6){$\scriptstyle E$}
\put( 5.3, 4.5){$\scriptstyle O$}
\put( 7.3, 6.7){$\scriptstyle M$}



\end{picture}
\PGrestore