Home | Proposed Problems | 1, 10, 20, 30, 40, 50, 60 | Previous, Next
 Problem 71. Cyclic Quadrilateral, Angles. Level: High School, SAT Prep, College


 Hints:
 Inscribed angle
 Cyclic quadrilateral

 

 

  

In a cyclic quadrilateral ABCD prove that each exterior angle is equal to the opposite interior angle.

 

HINTS:

PROPOSITION 1.  An inscribed angle is measured by one-half its intercepted arc.
 

DEFINITION. A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle.

PROPOSITION 2. Opposite angles of a cyclic (inscribed) quadrilateral are supplementary. Also converse.

PROPOSITION 3. A quadrilateral is cyclic if one side subtends congruent angles at the two opposite vertices. Also converse.

 

 

 

 
Home | Problems | Email

Last updated: February 23, 2008