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1. Circle O and circle P, with radii 3 and 5, respectively, are both tangent to line L at H. Enter all possible lengths of line OP separated by commas.

 

2. If angle B= 39 degrees and arc PS=116 degrees, find the degree measure of arc AS. 

https://latex.artofproblemsolving.com/1/4/0/14037dc6acf34cb7c5c1279737cdcdf86bd7751b.png

 

I keep getting 160 for number 2 but it was wrong.

 

CAN YOU PLZ HELP ME?

 Feb 27, 2019
 #1
avatar+194 
+1

1)

 

Circle O is a unit circle. Segment AS has length 12/5 and is tangent to circle O at A. If P is the intersection of OS with circle O, find length PS.

 

AS  = 12/5      AO  = 1

 

SO  =  sqrt [ (12/5)^2  + 1 ]  =   sqrt [  144 + 25] / 5  =  13/5

 

So...PS   =   SO  - PO  =   13/5  -  1  =     8/5

 

 

2)

 

Angle A: Angle P: Angle ASP are in ratio 1: 2: 2. Find the degree measure of angle BSA.

 

Angle A  =  36°......Angle P, ASP  =  72°

 

Angle  ASP  =  (1/2)minor arc AS  =  angle BSA  =  72°

 Feb 27, 2019
 #2
avatar+104 
+1

I'm confused. How does this relate to my question?

IneedHALP  Feb 28, 2019
 #3
avatar+99659 
+1

2  Secant-Tangent Theorem

 

Angle ABS =  (1/2) ( arc AS - arc AP)

39 = (1/2) (arc AS - arc AP)

78 = arc AS - arc AP   (1) 

 

arc AS + arc AP =  360 - arc PS

arc AS + arc AP = 360 - 116

arc AS + arc AP = 244   (2)

 

Using (1) and (2)  we have that

 

arc  AS - arc AP  =  78

arc AS + arc AP  =  244       add these

 

2arcAS = 322

arc AS = 161°

 

cool cool cool

 Feb 28, 2019
edited by CPhill  Feb 28, 2019
 #4
avatar+104 
0

I don't really understand. Can you explain to me in another way?

IneedHALP  Mar 1, 2019

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