Thread: Circle properties

Prove that ADOC is a cyclic quad if angle ABC = 17 and angle ADC = 34.



the proof quoted is that AOC is 34 (twice angle at circumference)
and as ADC = 34, must be angles standing on same arc. Hence must be cyclic quad.

my question is that the corollary of the twice angle at circumfernce is that if ADC is 34, it is twice angle on circumference, so does that mean it has to be at the centre?

It seems to me to be a theorem.

That given a circle with points A and B on the circle. If points C and D a chosen inside the circle such as
<ACB=<ADB
Then,
ABCD is a cyclis quadrilateral.