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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 8.2, Problem 27E
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Elementary Geometry for College St...

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

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercises 27 to 30, find the area of the figure shown.

Given: In ⊙ O , O A = 5 ,
B C = 6 , a n d
C D = 4
Find: A A B C D

Chapter 8.2, Problem 27E, In Exercises 27 to 30, find the area of the figure shown. Given: In O, OA=5, BC=6, and CD=4 Find:

To determine

To Find:

The area of the quadrilateral ABCD inscribed by the circle with centre 'O'.

Explanation

Formula Used:

Angle subtended by a diameter on any point of circle is 90°.

Pythagorean theorem for the right angle triangle ∆ABC for the hypotenuse AC,

AC2=AB2+BC2.

Area of right triangle =12×b×h

Calculation:

Consider the quadrilateral ABCD.

This quadrilateral can be divided into two triangles. That is, ∆ABC and ∆ADC.

By the angle subtended in a diameter of the circle theorem, it makes 90° at the m∠D and m∠B.

It is given that OA=5=radius, BC=6 and CD=4.

As radius is 5, the diameter is twice the radius.

CA=10

Consider the ∆ABC,

Here BC=6 and CA=10. Applying Pythagorean theorem,

CA2=AB2+BC2

102=AB2+62

AB2=100-36

AB=8 units

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Sect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10E
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