Given a circle O, OM is the
perpendicular bisector of AB, AC extended meets the circle at D,
BE extended meets the circle at F, DE extented and AB extended
meet at G, FC extended and BA extended meet at H. Prove that M is
the midpoint of HG.
View or post a solution.

HINTS:
PARALLEL LINES
Proposition. If two lines
are parallel, each pair of alternate interior angles are
congruent. Also converse.
ANGLES IN A CIRCLE
Proposition. An inscribed angle is
measured by onehalf its intercepted arc.
DIAMETER AND CHORD
Proposition. A diameter perpendicular to a
chord bisects the chord and its arcs..
TRIANGLE CONGRUENCE A.S.A. If
two angles and the included side of one triangle are congruent
to the corresponding parts of another, then the triangles are
congruent.
CYCLIC QUADRILATERAL is a quadrilateral whose
vertices all lie on a single circle.
Proposition 1.
Opposite angles of a cyclic (inscribed) quadrilateral are
supplementary. Also converse.
Proposition 2. A quadrilateral is cyclic if one side
subtends congruent angles at the two opposite vertices. Also
converse.
See:
Proposed Problem 77
