+123 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?
+193 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°
+129852 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°
