Question

Can someone help? I'm working on a Geometry proof. I have the first three steps, but I don't know where to go from there.

Answer 1

In the following figure, the small circle and the large circle have the same center O. Chord AB is tangent to the smaller circle at C. Prove that the area between the large and small circles is the same as the area of the circle that has AB as a diameter.

Answer 2

This is what I have so far, but I don't think its right.

Statements: Reasons:
1. O is the center of both 1. Given
a small and large circle.
Chord AB is tangent to C.

2. Construct line CO 2. Construction of radius of
smaller circle.

3. Angle OCB is 90 degrees 3. Intersecting Tangent and radius
(Theorem 7.11)

Answer 3

3.reason...it forms right angle

Answer 4

but all of your answers are correct

Answer 5

Okay. But now I have no idea where to go from Step 3.

Answer 6

OC = radius of small circle
area of small circle = pi(OC^2)
AC^2 + OC^2 = AO^2
AO = sqrt(AC^2 + OC^2) = radius of larger circle
area of lager circle = pi(AO^2) = pi(AC^2 + OC^2)
area between circle = area of big - area of small
pi(AC^2 + OC^2) - pi(OC^2)
= pi(AC^2)

area of of circle with diameter ab
= pi(AC^2)

both the same