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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?

IneedHALP Feb 27, 2019

#1**+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°

bigbrotheprodude Feb 27, 2019

#3**+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°

CPhill Feb 28, 2019