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Can someone solve this?

Can someone solve this?-example-1

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Answer:

  1. 32°
  2. C
  3. D
  4. A

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°

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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

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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

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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

User Nathan Teyou
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