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.

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

Manmeet Singh · Accepted Answer

With the given conditions, it is not possible to prove that QP = 2OS We can just prove that PR = 2OS

In Î”PQR, O is the mid point of QR (since O is the center of circle) Also, S is the mid point of PQ (radius perpendicular to chord bisects the chord) Now, using mid point theorem, We can say that OS = $\frac{1}{2} P R$ $\Rightarrow P R = 2 O S$ So, please recheck your query and do get back to us