CPhill

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Nombre de usuarioCPhill
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Preguntas 47
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 #1
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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   ....  

 

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°

 

3)

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

 

Angle B =  (1/2) ( arc AS - arc AP)

38  =  (1/2) (arc AS - arc AP)

76  =  arc AS - arc AP     (1)

 

And

arc AS + arc AP  + arc PS  = 360

arc AS + arc AP   +  116  =  360

arc AS  + arc AP  =  244   (2)

 

Add  (1)  and (2)

 

arc AS - arc AP   =  76

arc AS +  arc AP  = 244

 

2 arc AS  =  320      divide by 2

arc AS  =  160°

 

 

4)

Points A and B are on a circle centered at O, and point P is outside the circle such that PA and PB are tangent to the circle. If angle OPA = 32 degrees, then what is the measure of minor arc AB, in degrees?

 

Draw radii OA, OB...so  OAPB forms a quadrilaterlal....the sum of its interior angles = 360°

 

Angles OAP, OBP  =  90°  and OPA  =  32°, then angle BPA  =  64°

 

So...angle OAB  =  360 - 2(90) - 64  =  116°

 

And  OAB  is a central angle  intercepting minor arc AB, so its measure is also 116°

 

5)

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

 

{Need a pic, here  }

 

 

6)

Given regular pentagon ABCDE, a circle can be drawn that is tangent to DC at D and to AB at A. What is the number of degrees in minor arc AD?

 

Call the center of the circle O, connect  OA  and OD

And OABCD  forms another pentagon whose interior angles sum to 540°

Angles  ODC and angle OAB   =  90°

Angles DCB and CBA  =  108°

So  angle DOA  =  540 - 2(90) - 2(108)  = 144°  ...this is a central angle in the circle intercepting minor arc  AD  ....so it also measures 144°

 

 

cool cool cool

CPhill 20 mins ago