Question

In the figure , OS is perpendicular to the chord PQ of a circle whose centre is O. if QR is a diameter ,show that QP=2OS.

Answer 1

In triangle, PQR O is the midpoint of QR (since O is the center of circle)
Also, S is the midpoint of PQ 
If we use midpoint theorem
OS will be equal to 1/2 PR

PR = 2OS

Answer 2

Answer:

Step-by-step explanation:

OS ⊥ PQ

⇒ S is the mid-point of PQ. [The perpendicular drawn from the centre to a chord bisects the chord.]

 

Also, O is the mid-point of QR. [Centre of the circle and midpoint of the point of the diameter.]

 

Thus, in ΔPQR, S and O are mid-points of PQ and QR respectively.

Therefore, SO || PR and, SO = 1/2 PR    

[Line segment joining the mid-points of two sides of a triangle is half of the third side]  

∴ PR = 2OS.