Given a circle (1), the lines AED (2)
and BFC (3). If AB is parallel to CD, prove that the angles AFB
and AEB are equal.
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![Problem: Angles in a circle, parallel lines, cyclic quadrilateral](p077_circle_angle.gif)
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HINTS:
PARALLEL LINES
Proposition. If two lines
are parallel, each pair of alternate interior angles are
congruent. Also converse.
![](parallel_alternate.gif)
ANGLES IN A CIRCLE
Proposition. An inscribed angle is
measured by one-half its intercepted arc.
![](inscribed_angle.gif)
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.
![](cyclic_quadrilateral_1.gif)
Proposition 2. A quadrilateral is cyclic if one side
subtends congruent angles at the two opposite vertices. Also
converse.
![](cyclic_quadrilateral_2.gif)
See also:
Problem 71
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