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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 $\angle TOP = 45^{\circ}$, then what is the measure of minor arc $TU$, in degrees?

 Mar 24, 2024
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avatar+128794 
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                               T

                           45

                        O                             P                     

                          45

                              U

 

TP =  UP

TO = UO

PO = PO

Therefore  triangle  OPT   is  congruent to triangle OPU

Then angle TOP  = angle UOP = 45

Then arc TU =  angle TOP + angle UOP  =  90°

 

cool cool cool

 Mar 24, 2024

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