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?

Guest Feb 14, 2022

#1**+1 **

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°

CPhill Feb 14, 2022