Chapter 4.3, Problem 28E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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.

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...

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