Center of outscribed circle of triangle

[Jovana]

Hello.
I was doing a problem and there was a triangle with a point \(D\) inside it such that \(\angle ADB = 2 \angle ACB\). I concluded that \(D\) therefore must be the center of the outscribed circle of the triangle \(ABC\), because \(\angle ADB\) is the central angle of \(\angle ACB\). My proof was wrong, and someone told me I can't conclude from that that it's the center. Why is that so?

Thank you in advance. Sorry for my bad English, it's not my native language.

 

[pka]

Is your term outscribed circle what is also known as the circumcircle ?

 

[Dr.Peterson]

Given the angle ADB, D could be anywhere on the circle containing A, B, and the circumcenter O (the center of the circumscribed circle):



As pka pointed out, what you are calling the outcircle (presumably in contrast to the incircle) is called the circumcircle. There is also something called an excircle, which was what your term first called to mind.