a.
To calculate: The value x of
a.
Answer to Problem 5CR
The value of x is
Explanation of Solution
Given information:
A circle with two chords.
Formula used:
The below theorem is used:
Chord-Chord Power theorem states that if two chords of a circle intersect, then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord.
Calculation:
By chord- chord power theorem, we get
b.
To find: The value x of
b.
Answer to Problem 5CR
The value of x is
Explanation of Solution
Given information:
Side AB = 16,
Side BC = x ,
Side CD = 3 .
Side AD = 15.
Formula used:
The below theorem is used:
Corresponding sides of similar triangles are congruent.
Calculation:
△ABC and △ACD are similar triangles.
Corresponding sides of similar triangles are congruent.
c.
To find the measure of arc x .
c.
Answer to Problem 5CR
The measure of arc x is
Explanation of Solution
Given information:
Formula used:
The measure of secant-secant
Calculation:
d.
To find: The value of side x if one of the side AB is 4.
d.
Answer to Problem 5CR
The value of x is
Explanation of Solution
Given information:
Side AB = 4,
Side CB = 3,
Side AD = 13.
Formula used:
The below theorem is used:
Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.
In right angle triangle,
Proof:
Side AC can be calculated by applying Pythagoras Theorem.
In right angled triangle △ABC , we get
Side DC can be calculated by applying Pythagoras Theorem.
In right angled triangle △ACD , we get
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Geometry For Enjoyment And Challenge
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning