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Points T and U lie on a circle centered at O, and point P is outside the circle such that \(\overline{PT}\) and \(\overline{PU}\) are tangent to the circle. If \(\angle TPO = 26^{\circ},\) then what is the measure of minor arc TU, in degrees?

 Jun 7, 2020
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angle(TPO) = angle(UPO  =  26o     --->     angle(TPU  =  52o  

 

If minor arc(TU)  =  x,  then major arc(TU)  =  360o - x

 

angle(TPU)  =  ½·[ major arc(TU) - minor arc(TU) ]

             52o  =  ½·[ ( 360o - x ) - ( x )]

             52o  =  ½·[ 360o - 2x ]

             52o  =  180o - x

                 x  =  128o

 Jun 7, 2020

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