   Chapter 6.4, Problem 35E 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

Two congruent circles, ⊙ O and ⊙ P , do not intersect. Construct a common external tangent for ⊙ O and ⊙ P .

To determine

To construct:

A common external tangent for congruent circles O and P.

Explanation

Given:

Two congruent circles, O and P, do not intersect.

Properties Used:

The line that is perpendicular to the radius of a circle at its endpoint on the circle is a tangent to the circle. In the given figure, QT is a tangent to O at point T.

A tangent of two circles is a common external tangent if the intersection of the tangent and the line segment joining the centers is empty as shown in the figure below

Construction Strategy:

i) Draw the given congruent circles O and P, at some distance apart.

ii) Draw a line OP¯ through the two center points O and P.

iii) Construct perpendicular at point O intersecting the circle at X and M.

iv) Similarly, construct perpendicular at point P intersecting the circle at Y and N.

v) Join XY¯ and MN¯ which are the required tangent i

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