Question 91

In the given figure. PQR is an equilateral triangle and PS is the angle bisector of ∠P. What is the value of RT: RQ? 


We have 

Now PQR is an equilateral triangle 
so Angle PRQ=60
Now therefore angle QRT =180-60=120
Now PS bisects angle RPQ 
so angle RPS =30
Now RS is a chord so RPS=RQS =30
So in triangle RTQ 
angle RTQ =180-30-120=30
So we get Angle RTQ=RQT
So we can say RT=RQ

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