Please help me! I need help very fast i am very confused!

Question

Question 1: AB¯¯¯¯¯ and BC¯¯¯¯¯ are tangent to ⊙ O. Identify BC.

A.) 22

B.) 40

C.) 52

D.) 11

Question 2: Identify the arc length of AD◠ in terms of π.

A.) ≈ 5.09π in.

B.) ≈ 1.96π in.

C.) ≈ 3.91π in.

D.) ≈ 4.09π in.

Please give the explanations and the answers ASAP please!

Answer 1

Since the two segments that intersect OUTSIDE of the circle are both TANGENT to the circle (touch in just 1 point), there is some theorem that says they have the same length. So set their algebraic expressions equal.

2(3x-7) = 4x+8

6x - 14 = 4x + 8

2x = 22

x = 11, but they are asking for the length of segment BC, so must plug 11 back into 4x+8

so BC = 52

Arclength is radius*central angle (in radians). Need to convert the angle across from arcAD into radians.

Because it is a straight line with a 92 degree angle, the angle across from arcAD = 180 - 92 = 88 degrees.

This needs to be converted to radians: 88*pi/180 = pi(22/45) or (22/45)π

Now arclength is radius * (22/45)pi or (8)(22/45) pi = (176/45)π inches