   Chapter 6.2, Problem 40E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 39 to 47, provide a paragraph proof. Be sure to provide a drawing, Given, and Prove where needed.The line joining the centers of two circles that intersect at two points is the perpendicular bisector of the common chord.

To determine

To prove:

The given statement, “The line joining the centers of two circles that intersect at two points is the perpendicular bisector of the common chord.” by providing a paragraph proof.

Explanation

Proof:

 Statements Reason Given We have drawn O1O2¯, the common chord PQ¯, the intersection point R of these two lines. ΔO1PO2≅ΔO1QO2 Radii in the circle C1.O1P=O1QRadii in the circle C2.O2P=O2QBy Reflexive property,O1O2=O1O2SSS Congruence. m∠O2O1P=m∠O2O1Q In congruent triangles corresponding elements are congruent

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