Question

In the figure, 0 is the centre
circle. ZPOQ=50°, then what is the measure
of arc PXQ and arc PYQ?



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Answer 1

Answer:

Step-by-step explanation:

We know, that radius is perpendicular to a tangent .

∴  ∠OPR=90  

o

 

⇒  ∠OPQ+∠QPR=90  

o

 

⇒  ∠OPQ+50  

o

=90  

o

 

⇒  ∠OPQ=90  

o

−50  

o

 

⇒  ∠OPQ=40  

o

 

⇒  OP=OQ                                                            [ Radii of a circle ]

⇒  ∠OPQ=∠OQP=40  

o

                                 [ Base angles of equal sides are also equal ]

In △POQ,

⇒  ∠OQP+∠POQ+∠OPQ=180  

o

                    [ Sum of angles of a triangle is 180  

o

 ]

⇒  40  

o

+∠POQ+40  

o

=180  

o

 

⇒  ∠POQ+80=180  

o

 

⇒  ∠POQ=100  

o