Proposed Geometry Problem 77 Angles in a circle, Cyclic Quadrilateral, Parallel lines. College, SAT Prep. Elearning, Online math tutor

Problem 77. Angles in a circle, Cyclic Quadrilateral, Parallel lines. Level: High School, SAT Prep, College

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. Post your solutions or ideas in the blog.

Problem: Angles in a circle, parallel lines, cyclic quadrilateral

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 one-half its intercepted arc.

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.