[b]Lemma 1[/b]: Given a line [i]l[/i] and a point[i] P[/i] not on[i] l[/i], it is possible to construct a line [i]m[/i] through[i] P[/i] such that [i]m[/i] ||[i] l [/i]using only a straightedge.[br][br][list][*][b]Part A: [/b]Given a line[i] l[/i], points[i] A[/i], [i]B[/i], and their midpoint[i] M[/i] on[i] l[/i], and a point [i]P[/i] not on[i] l[/i], it is possible to construct a line [i]m[/i] through [i]P[/i] such that [i]m[/i] ||[i] l[/i] using only a straightedge. [/*][/list]

[list][*][b]Part B: [/b]Given a line[i] l, [/i]a point [i]P[/i] not on [i]l[/i], and a circle [i]c[/i] with center [i]O[/i], it is possible to construct a line[i] m[/i] through [i]P[/i] such that [i]m[/i] ||[i] l[/i] using only a straightedge. [/*][/list]