Asked by Amy

Points $A$ and $B$ are on a circle centered at $O$, and point $P$ is outside the circle such that $\overline{PA}$ and $\overline{PB}$ are tangent to the circle. If $\angle OPA = 32^{\circ}$, then what is the measure of minor arc $AB$, in degrees?
Answered by Reiny
Just use ordinary keyboard keys

According to the properties of tangents to circles,
AO is perpendicular to PA making angle PAO = 90°,
thus angle angle POA = 90-32 = 58°
The same property is true for angle POB
since PA = PB , angle POB = 58°
Then angle AOB = 116° and the arc AB is subtended by a central angle of 116°

or

PAOB is a quadrilateral with 2 right angles
thus angle AOB = 360° - 2(90)° - 64° = 116°
Answered by AoPS
Stop cheating! Please use our own message boards if you get stuck.
Answered by a nony mouse
lol i feel like the AoPS account is fake and looking for answers too
Answered by AoPS User
AoPS message boards are used for the same use as this website is used for. AoPS can track your IP address, and find out who you are. Next time, use the message boards.
Answered by AoPS
AoPS Admin and AoPS User, we appreciate that you are trying to stop people from cheating on AoPS homework, but unfortunately, no, we cannot track your IP address, nor do we care to do so. It is your choice if you decide to waste the homework questions, which are specifically designed to help you. And yes, if you're stuck the message boards are always open or you can privately ask your teacher if it is rather personal.
Answered by F AOPS
all u are fake
Answered by to them aops haters
DO we care
Answered by AoPS
i am real aops hahaha we actually reccomend using this cause aops message boards are very unrealiable so eys use this we encourage
Answered by AoPS
Please stop cheating!
Answered by AoPS
lol guys...thats not the right answer anyway
Answered by AoPS Person
Right that is wrong
Answered by Who cares?
Bruh do AoPS have trackers installed in everyone's devices? lol just asking.
Answered by bruh yall dum
yall know that aint the real aops right
Answered by I'm so sorry
I'm sorry AoPS if this is helping them cheat, but this serves the same purpose as the massage board and there is a high chance that nobody in the message board helped them. The correct answer is 128 degrees
Answered by AoPS
may your nuts forever be shriveled
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