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Solve the following exercises based on Principles 11-14, although an exercise may require the application of two or more of any of the principles. Round the answers to 3 decimal places where necessary unless otherwise stated.
a. If
b If
(a)
The value of DB and arc
Answer to Problem 20A
The value of DB is
Explanation of Solution
Given information:
AB = 5.378"
If the radius of the circle is perpendicular to the chord, it always divides the chord in two equal parts.
In the figure given above, the radius is perpendicular to the chord; hence, the parts AD will be equal to DB. Each portion AD and DB is half the value of part AB.
The value of DB is
If the radius of the circle is perpendicular to the chord, it always divides the chord and the arc cut off by the chord in two equal parts.
In the figure given above, the radius is perpendicular to the chord; hence, the parts AD will be equal to DB. Each portion AD and DB is half the value of part AB. Also, the arc cut off by the chord is divided in two equal parts.
The value of DB is
Conclusion:
Thus, the value of DB is
(b)
The value of AB and arc
Answer to Problem 20A
The value of AB is
Explanation of Solution
Given information:
AB = 3.017"
If the radius of the circle is perpendicular to the chord, it always divides the chord in two equal parts.
In the figure given above, the radius is perpendicular to the chord; hence, the parts AD will be equal to DB. Each portion AD and DB is half the value of part AB.
The value of AB is
If the radius of the circle is perpendicular to the chord, it always divides the chord and the arc cut off by the chord in two equal parts.
In the figure given above, the radius is perpendicular to the chord; hence, the parts AD will be equal to DB. Each portion AD and DB is half the value of part AB. Also, the arc cut off by the chord is divided in two equal parts.
The value of AB is
Conclusion:
Thus, the value of AB is
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Chapter 55 Solutions
Mathematics For Machine Technology
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