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eduard
3 years ago
15

Examine the diagram, where AB←→ is secant to the circle at points A and B, and CD←→ is secant to the circle at points C and D. T

he lines intersect inside the circle at point P, which is not the center.
A circle with no center shown and two secants as described in the text. Segment B P equals 6, segment C P equals 7, and segment D P equals 12.


What is the length of AP¯¯¯¯¯¯¯¯?
Enter the correct value.

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
5 0

In the secant secant theorem,

AP × BP = CP × DP

AP × 6 = 7 × 12

AP = 7 × 2 = 14

Answer: 14

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Answer:  117.6° ;  32.4° .
_________________________
Explanation:
_______________________________________________________
Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles.   
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We are given the following:
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We have a triangle.

Angle 1:  m∡1 = (8x) ;

Angle 2:  m∡2 = (2x + 3) ;

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We are asked to find:  "m∡1"  and " m∡2" .
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Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees.
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   So, " m∡1 + m∡2 + m∡3 = 180 " . 
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Let us substitute our given values for the measurements in EACH of
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                m∡1 + m∡2 + m∡3 = 180  ; 
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             8x + (2x + 3) + 30 = 180 ;
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             8x + 2x + 3 + 30 = 180 ;
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  Combine the "like terms" on the 'left-hand side" of the equation; to simplify:
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            +8x + 2x = +10x ;
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              +3 + 30 = +33 ; 
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  Rewrite the entire equation, as:
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         10x + 33 = 180 ; 
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 Now, subtract "33" from EACH SIDE of the equation:
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         10x + 33 − 33 = 180 −<span> 33 ;
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 to get:
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         10x    =   147 ;  
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   Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" : 
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         10x / 10 = 147 / 10 ; 
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   to get: 
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              x = 14.7 ;
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    Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m</span>∡1" and "m∡2";  as follows:
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Angle 1:  "(8x)" = 8*(14.7) =  117.6° ; 
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Angle 2:  "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ;
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These are the two answers; that is the 2 (TWO) values asked for in the question:   117.6° ;  32.4° .
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 Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m</span>∡3 = 30°); all add up to 180° ?
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Let us check:
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   m∡1  +  m∡2  +  m∡3 = 180 ; 
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Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true?
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   → 117.6 + 32.4 + 30 = ? 180 ??
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   → 117.6 + 32.4 = 150  ;   → 150 + 30 =? 180 ?  Yes!
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Step-by-step explanation:

Step by step answer

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