Inscribed angles and their measure

[smith]

If B is a point on circle O not on arc AC, an arc of circle O. Find measure of arc AC if measure of angle ABC is 60.

Can you please show your work? I'm completely stumped. Thanks.

[winsome]

Measure of arc AC = twice the measure of the inscribed angle ABC
Measure of arc AC = 2 (60)
Measure of arc AC = 120 degree.


To learn more you may click the link below and go through video lesson on ‘Inscribed angles and their measure':
http://www.winpossible.com/lessons/Geometry_Circles-_arcs,_chords,_tangents,_sector,_segment,_secant.html
Hope this helps

[Guest]

Thanks for you ....
The links given was too good and useful for me and i learned very much from that such as radius of circle, area of it's

[leesajohnson]

ABC angel is given = 60 degree
AC=?
AC= 2ABC
AC= 2(60)
AC= 120 degree.

[Guest]

Not sure that the original question is stated correctly.???

If AC are 2 points on an arc of circle O. This cuts the circle into 2 arcs, a major arc and a minor arc. and a stright line joining A to C is a chord of the circle cutting it into 2 segments, a minor segment and a major segment. So AC describes either arc. They are either equal in length or one is longer than the other. The question states B is a point on circle O, "NOT ON ARC AC" ,???, but if it is on the circle O it must be either on the major arc AC or on the minor arc AC. We know the angle ABC is 60 degrees so it must be on the major arc AC. The point B can be any point between A and C on the major arc AC. The angle subtended from AC to anywhere on the circumference of the major arc (60 degrees) is half the angle subtended to the centre within the minor arc. So the measure of the minor arc AC is the angle AOC and is 120 degrees.