Try the fastest way to create flashcards
Question

For each of the following statements, prove the statement if it is true or give a counterexample if it is false. a. The midpoint of the common chord of two circles that intersect in two points lies on the line through the centers of the circles. b. If inscribed angle ABC\angle A B C in a circle with center O measures 120120^{\circ}, then central angle AOC\angle A O C measures 120120^{\circ}. c. The angle bisector of any angle inscribed in a circle contains the center of the circle. d. If the line through the midpoints of two chords of a circle contains the center of the circle, then the chords are parallel.

Solution

Verified
Answered 2 years ago
Answered 2 years ago
Step 1
1 of 4

a. This is true. The following can be proven through an illustration: (Plotted using a graphing calculator) 'slader' As shown on the illustration, the midpoint PP of the common chord of the two circles coincides with the line that connects the centers of the two circles.

Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

Core Plus Mathematics, Course 3, Student Edition 1st Edition by McGraw-Hill

Core Plus Mathematics, Course 3, Student Edition

1st EditionISBN: 9780076657964 (1 more)McGraw-Hill
1,241 solutions
Cambridge IGCSE Mathematics Core and Extended 4th Edition by Ric Pimentel

Cambridge IGCSE Mathematics Core and Extended

4th EditionISBN: 9781510421684Ric Pimentel
1,758 solutions
Big Ideas Math Integrated Mathematics II 1st Edition by Boswell, Larson

Big Ideas Math Integrated Mathematics II

1st EditionISBN: 9781680330687Boswell, Larson
4,539 solutions
Big Ideas Math Integrated Mathematics III 1st Edition by Boswell, Larson

Big Ideas Math Integrated Mathematics III

1st EditionISBN: 9781680330878Boswell, Larson
3,800 solutions

More related questions

1/4

1/7