   Chapter 7.2, Problem 31E 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

Draw a triangle. Construct its inscribed circle.

To determine

To draw:

The triangle constructs its inscribed circle.

Explanation

Procedure used:

STEP 1: We start with the triangle ABC.

STEP 2: Place the compasses point on any of the triangle's vertices. Adjust the compasses to a medium width setting. The exact width is not important. Without changing the compasses' width, strike an arc across each adjacent side.

STEP 3: Change the compasses width if desired, then from the point where each arc crosses the side, draw two arcs inside the triangle so that they cross each other, using the same compasses width for each.

STEP 4: Using the straightedge, draw a line from the vertex of the triangle to where the last two arcs cross.

STEP 5: Repeat all of the above at any other vertex of the triangle. You will now have two new lines drawn. Where the two new lines intersect, mark a point as the incenter of the triangle.

STEP 6: Draw the perpendicular from the incenter to a side of the triangle. Label the point where it meets the side M.

STEP 7: Place the compasses on the incenter and set the width to point M. This is the radius of the incircle, sometimes called the inradius of the triangle. Draw a full circle. This is the incircle of the triangle.

Given:

Draw a triangle. Construct its inscribed circle.

Clarification:

STEP 1: We start with the triangle A, B, C.

STEP 2: Place the compasses point on the triangle's vertices B. Adjust the compasses to a medium width setting. The exact width is not important. Without changing the compasses' width, strike an arc across each adjacent side.

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