   Chapter 6.4, Problem 9E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Construct a circle O and choose some point D on the circle. Now construct the tangent to circle O at point D .

To determine

To construct:

A circle and choose a point on the circle and draw the tangent to the circle at this point.

Explanation

Given:

A circle O and some point D on the circle.

Approach:

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.

Construction Strategy:

i) Draw a circle O with radius r.

ii) Draw a point D on the circle.

iii) Draw a line connecting the point D to the center of the circle O and extend it outside the circle.

iv) Construct the perpendicular bisector of line OD. Start by placing the compass at D and adjusting the compass to any length <OD. Draw two arcs to intersect OD at Y and Z. Now draw arcs above and below the line from points Y and Z.

v) Place ruler where the arcs cross, and draw the line segment

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