Question

O is the center of the circle with the diameter of 10cm.PQ=1cm.Find the length of RS

Answer 1

Diameter of circle =10 cm

Radius of circle =r=  

2

10

​  

=5 cm

Thus OQ=OR=r=5 cm

⇒OQ=OP+PQ

⇒5=OP+1

⇒OP=4 cm

Applying pythagoras theorem in △ORP, we have

(OR)  

2

=(RP)  

2

+(PO)  

2

 

⇒(5)  

2

=(RP)  

2

+(4)  

2

 

⇒(RP)  

2

=9

⇒RP=3

Perpendicluar from the centre to a chord of circle bisects the chord.

Therefore, RS=2RP

⇒RS=2×3=6 cm