os is a perpendicular to the chord pq of a circle whose centre is o. if qr is the diameter show that qp=2os

 

Dear student,

 

Correction in your question: To prove : pr = 2os

 

Since os is perpendicular to pq and the perpendicular drawn from the centre to a chord bisects the chord.

s is the mid-point of pq.

Also, o being the centre, is the mid point of qr.

Thus, in triangle pqr, s and o are mid-points of pq and pr respectively.

Thus, os is parallel to pr

And, os = 1/2 pr  [since segment joining the mid-points of two sides of a triangle is half of the third side]

 

thus, pr = 2os

 

Requesting you to provide the other question in detail.

 

Yopper's Team