Question

In the figure alongside, PQ and RS are two chords interesting at T in a circle with centre O. If OT is the bisector of angle PTR, prove that :
i) PT=RT
ii) ST=TQ

PUT ONLY THE ATTACHMENT WHICH HAS EVERY STEP CLEARLY SHOWN WITH PROPER LANGUAGE. ​

Answer 1

Answer:

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Step-by-step explanation:

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  

o

 

2∠PSR=180  

o

 

∠PSQ=∠PSR=90  

o

 

then, RS=QS and ∠PSR=90  

o

 

PS is the perpendicular bisector of chord RQ

PS passes through center of circle.

Answer 2

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