Answer:
- 32°
- C
- D
- A
Step-by-step explanation:
1. The angle facing the given arcs is half their sum, so is (180 +116)/2 = 148°. Angle 1 is the supplement of this, ...
angle 1 = 180° -148° = 32°
__
2. Short arc WY is the supplement of 70°, Long arc WVY is the difference of that and 360°:
arc WVY = 360° -(180° -70°) = 180°+70°
arc WVY = 250° . . . . . matches choice C
__
3. Call the point of intersection of the secants X. The rule for secants is ...
(XA)(XC) = (XB)(XD)
So, the length XC is ...
XC = (XB)(XD)/(XA) = 2.4
and ...
AC = XA +XC = 3.2 +2.4 = 5.6 . . . . . matches choice D
__
4. As in problem 3, the product of lengths from the point of secant intersection to the points of circle intersection is the same for both secants.
(NQ)(NR) = (NP)(NS)
Substituting segment sums where necessary, we have ...
NQ(NQ +QR) = NP(NP +PS)
Solving for PS, we have ...
PS = NQ(NQ +QR)/NP - NP . . . . . matches choice A
