Points $A$ and $B$ are on circle $O$ such that arc $AB$ is 80 degrees. A circle is constructed that passes through $A$, $B$, and $O$. Find the measure of arc $AOB$ on this circle.

AdminMod2  Aug 26, 2017

1+0 Answers




Draw OA , OB and AB


Now since minor arc AB  = 80°....then, in triangle AOB,   since angle AOB is a central angle of the larger  circle  subtending minor arc AB, it  has the same measure.


And OA  = OB  since they are both radii of the larger circle....but if OA  = OB....then the angles opposite these sides in triangle AOB - namely angles OAB and OBA - are equal.... 


Thus....  OAB  = OBA  =   [ 180 - 80 ] / 2   = 50°


But angles OAB and OBA are inscribed angles in the smaller circle

And OAB  intercepts minor arc OB.....and its measure is twice that of OAB  =100°


Likewise....OBA  intercepts minor arc OA....and its measure is twice that of OBA  = 100°


Thus  minor arc OA  + minor arc OB  =  arc AOB

And    100° + 100°  =  arc AOB  = 200°



cool cool cool

CPhill  Aug 26, 2017

9 Online Users

New Privacy Policy (May 2018)
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  Privacy Policy