Question

In the given fig PQ and PS are two chords of a circle whose center is o such that angle QPO = angleSPO prove that CQ =Ps​

Answer 1

Answer:

• Given, chords RP=RQ
• In △PSQ and △PSR
• PQ=PR (given)
• ∠RPS=∠QPS (given)
• PS=PS (common)
• △PSQ≅△PSR (by SAS)
• ⇒RS=QS
• ∠PSR=∠PSQ
• But,
• ∠PSR+∠PSQ=180°
•  2∠PSR=180°  
• ∠PSQ=∠PSR=90  °
• then, RS=QS and ∠PSR=90  °
•  PS is the perpendicular bisector of chord RQ
• PS passes through center of circle.