BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
4 views

A circle can be inscribed in the trapezoid shown. Find the area of that circle.

Chapter 8.5, Problem 27E, A circle can be inscribed in the trapezoid shown. Find the area of that circle.

To determine

To find:

Area of circle inscribed in a trapezoid.

Explanation

Formula:

If r is the radius of circle,

Acircle=πr2.

Calculation:

Consider the following diagram in which ABCD is a trapezoid with an inscribed circle.

Two perpendiculars AM and DN have been drawn from vertices A and D of the trapezoid.

Consider AMB and DNC.

In these two triangles, AB=DC=13

AMB=DNC=90°.

We know that the distance between parallel lines is same.

Hence, AM=DN.

From the above observations, it is clear that AMBDNC by RHS (right-angle hypotenuse side) test of congruency.

We know that, if two triangles are congruent then their corresponding sides are also equal.

Hence, BM=NC.

In quadrilateral AMND, AM=DN and AMN=DNM=90°,

Hence, AMND is a rectangle.

Opposite sides of a rectangle are equal. Therefore, AD=MN=8

Points M and N lie on BC. Hence, BC can be written as the sum of three segments.

BC=BM+MN+NC

18=BM+8+NC

Thus, BM+NC=18-8=10

Since, BM=NC

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
Sect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-31ESect-8.1 P-32ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.1 P-47ESect-8.1 P-48ESect-8.1 P-49ESect-8.1 P-50ESect-8.1 P-51ESect-8.1 P-52ESect-8.1 P-53ESect-8.1 P-54ESect-8.1 P-55ESect-8.1 P-56ESect-8.2 P-1ESect-8.2 P-2ESect-8.2 P-3ESect-8.2 P-4ESect-8.2 P-5ESect-8.2 P-6ESect-8.2 P-7ESect-8.2 P-8ESect-8.2 P-9ESect-8.2 P-10ESect-8.2 P-11ESect-8.2 P-12ESect-8.2 P-13ESect-8.2 P-14ESect-8.2 P-15ESect-8.2 P-16ESect-8.2 P-17ESect-8.2 P-18ESect-8.2 P-19ESect-8.2 P-20ESect-8.2 P-21ESect-8.2 P-22ESect-8.2 P-23ESect-8.2 P-24ESect-8.2 P-25ESect-8.2 P-26ESect-8.2 P-27ESect-8.2 P-28ESect-8.2 P-29ESect-8.2 P-30ESect-8.2 P-31ESect-8.2 P-32ESect-8.2 P-33ESect-8.2 P-34ESect-8.2 P-35ESect-8.2 P-36ESect-8.2 P-37ESect-8.2 P-38ESect-8.2 P-39ESect-8.2 P-40ESect-8.2 P-41ESect-8.2 P-42ESect-8.2 P-43ESect-8.2 P-44ESect-8.2 P-45ESect-8.2 P-46ESect-8.2 P-47ESect-8.2 P-48ESect-8.2 P-49ESect-8.2 P-50ESect-8.2 P-51ESect-8.2 P-52ESect-8.2 P-53ESect-8.2 P-54ESect-8.2 P-55ESect-8.2 P-56ESect-8.3 P-1ESect-8.3 P-2ESect-8.3 P-3ESect-8.3 P-4ESect-8.3 P-5ESect-8.3 P-6ESect-8.3 P-7ESect-8.3 P-8ESect-8.3 P-9ESect-8.3 P-10ESect-8.3 P-11ESect-8.3 P-12ESect-8.3 P-13ESect-8.3 P-14ESect-8.3 P-15ESect-8.3 P-16ESect-8.3 P-17ESect-8.3 P-18ESect-8.3 P-19ESect-8.3 P-20ESect-8.3 P-21ESect-8.3 P-22ESect-8.3 P-23ESect-8.3 P-24ESect-8.3 P-25ESect-8.3 P-26ESect-8.3 P-27ESect-8.3 P-28ESect-8.3 P-29ESect-8.3 P-30ESect-8.3 P-31ESect-8.3 P-32ESect-8.3 P-33ESect-8.3 P-34ESect-8.3 P-35ESect-8.3 P-36ESect-8.3 P-37ESect-8.3 P-38ESect-8.4 P-1ESect-8.4 P-2ESect-8.4 P-3ESect-8.4 P-4ESect-8.4 P-5ESect-8.4 P-6ESect-8.4 P-7ESect-8.4 P-8ESect-8.4 P-9ESect-8.4 P-10ESect-8.4 P-11ESect-8.4 P-12ESect-8.4 P-13ESect-8.4 P-14ESect-8.4 P-15ESect-8.4 P-16ESect-8.4 P-17ESect-8.4 P-18ESect-8.4 P-19ESect-8.4 P-20ESect-8.4 P-21ESect-8.4 P-22ESect-8.4 P-23ESect-8.4 P-24ESect-8.4 P-25ESect-8.4 P-26ESect-8.4 P-27ESect-8.4 P-28ESect-8.4 P-29ESect-8.4 P-30ESect-8.4 P-31ESect-8.4 P-32ESect-8.4 P-33ESect-8.4 P-34ESect-8.4 P-36ESect-8.4 P-37ESect-8.4 P-38ESect-8.4 P-39ESect-8.4 P-40ESect-8.4 P-41ESect-8.4 P-42ESect-8.4 P-43ESect-8.4 P-44ESect-8.4 P-45ESect-8.4 P-46ESect-8.4 P-47ESect-8.5 P-1ESect-8.5 P-2ESect-8.5 P-3ESect-8.5 P-4ESect-8.5 P-5ESect-8.5 P-6ESect-8.5 P-7ESect-8.5 P-8ESect-8.5 P-9ESect-8.5 P-10ESect-8.5 P-11ESect-8.5 P-12ESect-8.5 P-13ESect-8.5 P-14ESect-8.5 P-15ESect-8.5 P-16ESect-8.5 P-17ESect-8.5 P-18ESect-8.5 P-19ESect-8.5 P-20ESect-8.5 P-21ESect-8.5 P-22ESect-8.5 P-23ESect-8.5 P-24ESect-8.5 P-25ESect-8.5 P-26ESect-8.5 P-27ESect-8.5 P-28ESect-8.5 P-29ESect-8.5 P-30ESect-8.5 P-31ESect-8.5 P-32ESect-8.5 P-33ESect-8.5 P-34ESect-8.5 P-35ESect-8.5 P-36ESect-8.5 P-37ESect-8.5 P-38ESect-8.5 P-39ESect-8.5 P-40ESect-8.5 P-41ESect-8.5 P-42ESect-8.5 P-43ESect-8.5 P-44ESect-8.5 P-45ESect-8.CR P-1CRSect-8.CR P-2CRSect-8.CR P-3CRSect-8.CR P-4CRSect-8.CR P-5CRSect-8.CR P-6CRSect-8.CR P-7CRSect-8.CR P-8CRSect-8.CR P-9CRSect-8.CR P-10CRSect-8.CR P-11CRSect-8.CR P-12CRSect-8.CR P-13CRSect-8.CR P-14CRSect-8.CR P-15CRSect-8.CR P-16CRSect-8.CR P-17CRSect-8.CR P-18CRSect-8.CR P-19CRSect-8.CR P-20CRSect-8.CR P-21CRSect-8.CR P-22CRSect-8.CR P-23CRSect-8.CR P-24CRSect-8.CR P-25CRSect-8.CR P-26CRSect-8.CR P-27CRSect-8.CR P-28CRSect-8.CR P-29CRSect-8.CR P-30CRSect-8.CR P-31CRSect-8.CR P-32CRSect-8.CR P-33CRSect-8.CR P-34CRSect-8.CR P-35CRSect-8.CR P-36CRSect-8.CR P-37CRSect-8.CR P-38CRSect-8.CR P-39CRSect-8.CR P-40CRSect-8.CT P-1CTSect-8.CT P-2CTSect-8.CT P-3CTSect-8.CT P-4CTSect-8.CT P-5CTSect-8.CT P-6CTSect-8.CT P-7CTSect-8.CT P-8CTSect-8.CT P-9CTSect-8.CT P-10CTSect-8.CT P-11CTSect-8.CT P-12CTSect-8.CT P-13CTSect-8.CT P-14CTSect-8.CT P-15CTSect-8.CT P-16CTSect-8.CT P-17CT

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Alzheimers Disease The projected number of people aged 65 and over in the U.S. population with Alzheimers disea...

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

Add: 2.147+2.04+60+0.007+0.83

Elementary Technical Mathematics

Use the guidelines of Section 4.5 to sketch the curve. y = (x 2)ex

Single Variable Calculus: Early Transcendentals, Volume I

The solution to dydt=ky, where k is a constant and P0 is the value of y when t = 0, is a) y = ekt b) y = xekt c...

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

Self Check Factor: p364.

College Algebra (MindTap Course List)