   Chapter 6.4, Problem 34E 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

A tangent E T ¯ is constructed to circle Q from external point E . Which angle and which side of triangle Q T E are largest? Which angle and which side are smallest?

To determine

To find:

The angle and side of triangle QTE that are largest and smallest.

Explanation

Given:

A tangent ET¯ is constructed to circle Q from external point E.

Theorem Used:

According to the Pythagorean theorem, in a right-angled triangle

hypotenuse2=base2+perpendicular2.

Property Used:

The angle formed by radius drawn to tangent equals 90°.

The hypotenuse is the longest side of a right- angled triangle, which is always opposite the right-angle.

Calculation:

In the figure below, a tangent ET¯ is constructed to circle Q from external point E.

Since, the angle formed by radius drawn to tangent equals 90° i.e. QT¯TE¯

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