The radius of two concentric circles, the radius of the big circle, the opposite extension lines of OA and ob intersect the small circle at C and D respectively. It is proved that AB is parallel to CD

The radius of two concentric circles, the radius of the big circle, the opposite extension lines of OA and ob intersect the small circle at C and D respectively. It is proved that AB is parallel to CD

It is proved that the radius of the big circle is R1 and the radius of the small circle is R2
AO=BO=R
So Ao: Bo = 1:1
And co = do = R2, so Co: do = 1:1
Angle boa and angle doc are opposite vertex angles, so angle boa = angle doc
So triangle AOB is similar to triangle doc
So angle Bao = angle DCO
So the line AB is parallel to the line DC

In the two concentric circles with point o as the center, the radii OA and ob of the big circle intersect the small circle a ', B', respectively?
A. AB=A'B'
B. The length of arc AB = the length of arc a'B '
C arc AB = arc a'B '
Degree of arc AB = degree of arc a'B '

D

As shown in the figure, in the two concentric circles with o as the center, the chord AB and CD of the big circle are equal, and AB and the small circle are tangent at point E

Prove: as shown in the right figure, connect OE, make of ⊥ CD through o at f. ∵ AB and small ⊙ o tangent at point E, ∵ OE ⊥ AB, ∵ AB = CD, ∵ OE = of (the chord center distance of the same circle is equal), and ∵ CD is tangent to small ⊙ o