Please solve question no 8 with proper explanation 

Asked by adityaahuja099 | 20th Nov, 2017, 07:54: PM

Expert Answer:

 
begin mathsize 16px style Consider space PR space as space straight a space chord space of space circle. space
Take space any space point space straight S space on space major space arc space of space circle. space
Now space PQRS space is space straight a space cyclic space quadrilateral. space
angle PQR space plus space angle PSR space equals 180 degree space space space space left parenthesis Opposite space angles space of space cyclic space quadrilateral right parenthesis
rightwards double arrow angle PSR space equals 180 degree space minus space 100 degree space equals space 80 degree
We space know space that space angle space subtended space by space an space arc space at space centre space is space double space the space angle
space subtended space by space it space any space point space on space the space remaining space part space of space the space circle. space space
rightwards double arrow angle POR space equals space 2 angle PSR space equals space 2 space left parenthesis 80 degree right parenthesis space equals space 160 degree space
In space triangle POR comma
OP space equals space OR space space space space space space space space space space space space space space space space space left parenthesis radii space of space same space circle right parenthesis space space space
angle OPR space equals space angle ORP space space space space left parenthesis Angles space opposite space equal space sides space of space straight a space triangle right parenthesis space
angle OPR space plus space angle ORP space plus space angle POR space equals space 180 degree space space space space left parenthesis Angle space sum space property space of space straight a space triangle right parenthesis
rightwards double arrow 2 angle OPR space plus space 160 degree equals space 180 degree
rightwards double arrow 2 angle OPR space equals 180 degree space minus space 160 degree space equals space 20 degree
rightwards double arrow angle OPR space equals 10 degree space end style

Answered by Rashmi Khot | 30th Nov, 2017, 10:10: AM