Question

C.1. In the adjoining figure, i) Chord PR =chord QS ii) O is the centre of the circle Prove that ZPOR = ZQOS​

Answer 1

Answer:

hey here is your proof

so pls mark it as brainliest

kindly refer the reference diagram uploaded above for better understanding

Step-by-step explanation:

so here for given circle with centre O

chord PR=chord QS

so as we know that if the corresponding chords of given circle are congruent then its corresponding arcs are also equal

thus then m(arc pr)=m(arc qs) (1)

so here angle por and angle qos are two respective central angles of given circle

so we know that the arc intercepted ie subtended by central angle on circumference of circle is of same measure as that of central angle

thus angle por=m(arc pr)

angle qos=m(arc qs)

but m(arc pr)=m(arc qs) from (1)

thus we can conclude that

angle por=angle qos by definition of congruency between two corresponding arcs and central angle of a particular circle

hence angle por=angle qos

thus proved