   Chapter 6.4, Problem 10E 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

Construct a circle P and choose three points R , S , and T on the circle. Construct the triangle that has its sides tangent to the circle at R , S , and T .

To determine

To construct:

A circle and choose three points on the circle and draw the triangle that has its sides tangent to the circle at these three points.

Explanation

Concept:

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.

Given:

A circle P and three points R, S, and T on the circle.

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. This is the tangent to the circle.

Construction:

Drawing a circle P with radius r=2cm and a point R on the circle. Connecting the point R to the center of the circle P and extending it outside the circle

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