   Chapter 4.3, Problem 28E 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

Which type(s) of quadrilateral(s) is (are) necessarily cyclic? a) A kite b) A rectangle

To determine

To find:

The type(s) of quadrilateral(s) is (are) necessarily cyclic.

Explanation

Quadrilateral means four-sided figure. Put them together, and we get the definition for cyclic quadrilateral: any four-sided figure (quadrilateral) whose four vertices (corners) lie on a circle.

Property of cyclic quadrilateral:

The sum of opposite angles of a cyclic quadrilateral 180 degrees.

In other words, angle A + angle C = 180, and angle B + angle D = 180

Calculation:

To find a kite is necessarily cyclic or not:

When a kite is a cyclic quadrilateral (all four vertices lie on a circle), it must be composed of two congruent right triangles. This type of kite is known as a right kite.

A kite does have an in-circle i.e. a circle inscribed in it.

The cyclic kite and its in-circle is shown in given figure:

So, a kite is cyclic quadrilateral when its right kite.

To find a rectangle is necessarily cyclic or not:

If the quadrilateral is a cyclic quadrilateral, then all vertices of a quadrilateral lie on a circle...

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 23-36, find the domain of the function. 26. g(x)=2x+1x1

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

True or False: n=1(1)nnn+3 converges.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

π does not exist

Study Guide for Stewart's Multivariable Calculus, 8th 