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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

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

Construct the two tangent segments to circle P (not shown) from external point E .

To determine

To construct:

Two tangent segments to a circle from an external point.

Explanation

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:

The circle P and an external point E.

Construction Strategy:

i) Draw a circle P with radius r.

ii) Take an external point E and draw EP¯ .

iii) Construct the perpendicular bisector of line EP¯. Start by placing the compass at E and adjusting the compass to any length <EP¯. Draw two arcs above and below the line from points E and P. Let the midpoint be M.

iv) With M as center and MP¯ (or ME¯) as the radius, construct a circle. Place ruler where the circles intersect, and draw the line segments T and V from point E. ET¯ or EV¯ is the desired tangent

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