# Geometry

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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?

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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°

• Geometry -

Stop cheating! Please use our own message boards if you get stuck.

• Geometry -

lol i feel like the AoPS account is fake and looking for answers too

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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.

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