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MTH 338 Homework #3
#6 PQ perpendicular to the tangent line at the point of tangency
#11 Prove that the perpendicular bisectors of a cyclic quadrilateral are concurrent if and only if the quadrilateral is cyclic.
#16 The three excircles of trian...
#22 Prove if two circles are orthogonal, then they intersect at exactly two points and their tangents are perpendicular at both of those points
Playfair's postulate is logically equivalent to the statement: If a line intersects one of two parallel lines, then it also intersects the other
Euclid's fifth postulate is logically equivalent to the statement: If t is a transversal to l and m, l parallel to m and t perpedicular to l, then tis perpendicular to m
MTH 338 Homework #3
Author:
Bill OConnell
Homework 3 #6, 11, 16, 22 Equivalence to Euclid's 5th postulate.
#6 PQ perpendicular to the tangent line at the point of tangency
#11 Prove that the perpendicular bisectors of a cyclic quadrilateral are concurrent if and only if the quadrilateral is cyclic.
#16 The three excircles of trian...
#22 Prove if two circles are orthogonal, then they intersect at exactly two points and their tangents are perpendicular at both of those points
Playfair's postulate is logically equivalent to the statement: If a line intersects one of two parallel lines, then it also intersects the other
Euclid's fifth postulate is logically equivalent to the statement: If t is a transversal to l and m, l parallel to m and t perpedicular to l, then tis perpendicular to m
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