PQ and RQ are the two chords of a circle equidistant from the centre O. Prove that the diameter passing through Q bisects begin mathsize 12px style angle end stylePQR and begin mathsize 12px style angle end stylePSR.



Asked by Topperlearning User | 18th Aug, 2017, 08:40: AM

Expert Answer:

 
begin mathsize 12px style Given space colon space PQ space and space QR space are space two space chords space equidistant space from space the space centre.
To space prove colon space Diameter space QS space bisects space angle PQR space and space angle PSR
Construction colon space Join space PS space and space RS
Since comma space chords space equidistant space from space the space centre space are space equal
PQ equals RQ
In space increment PQS space and space increment RQS
PQ equals RQ
angle QPS equals angle QRS space space space space space left parenthesis each space is space straight a space right space angle right parenthesis
QS equals QS
increment PQS approximately equal to increment RQS space space space space space space left parenthesis RHS right parenthesis
angle PQS equals angle RQS space and space angle PSQ equals angle RSQ space space space space left parenthesis straight c. straight p. straight c. straight t right parenthesis
QS space bisects space angle PQR space and space angle PSR end style

Answered by  | 18th Aug, 2017, 10:40: AM