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Points A and B are on a circle centered at O, and point P is outside the circle such that PA and PB are tangent to the circle. If angle OPA = 30 degrees, then what is the measure of minor arc AB, in degrees?

 

 Feb 14, 2022
 #1
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Connect  AO,  BO , PO

 

Tangents drawn from a single point outside a circle are equal

 

OP = OP

AO = BO

AP = BP

 

So by SSS.....triangles APO and BPO  are congruent

 

Then because angle OPA = 30° then angle  APB = 60°

 

And angle AOB is supplemental to angle APB =  120°

 

And central angle APB = measure of minor arc AB = 120°

 

 

cool cool cool

 Feb 14, 2022

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