#### Question

# 10 points 3 questions help please?

12. In circle G, arc NA is congruent to arc AL. What is the measure of ANL?

http://i54.tinypic.com/ih7gig.gif

8. Which of the following angles is formed by a tangent and secant in circle I?

http://i53.tinypic.com/1q21l0.gif

3. What is the measure of arc AC?

http://i56.tinypic.com/30b3dpu.jpg

I will reward best answer please help me

#### Answer

12.

Since AN and AL are equal, each must be 180/2 = 90 degrees

why 180 ? coz its a half of a circle (360/2 = 180)

ANL = AN +NL = 90 +180 = 270 degrees or 3pi/2 in rads for the arc

8.

<DEF, since it is the only angle in contact with a tangent (you could also say AEF, HEF, & IEF they are all the same)

3. The triangle shown here is an equilateral triangle. Therefore, the angles of the triangle should be 60 degrees (all of them).

Remember the inscribed angle theorem?

Inscribed angle = ?intercepted angle/arc

?AC = <ARC

AC = 60(2) = 120 or 2pi/3 rads

1. ANL =45

2. ADF

3. equilateral

12. 45° because tan(ANL) = AG/GV = R/R = 1

8. AEF

3. 2/3*pi*R because at the center of the circle we have three times 120° = 2/3*pi