Question

A chord PQ of circle is parallel to the tangent drawn at a point R of the circle. prove that R bisects the arc PRQ

Answer 1

see beloww for answer

please mark me as brainlest

Answer 2

Given:

PQ || M 

To Find:

Prove R bisects the arc PRQ.

Solution:

Construction - Join OR intersecting PQ at M

Thus, OR ⊥ M ( Radius is perpendicular to the tangent at point contact)

∠OSP = ∠OSQ = 90° corresponding angles 

In ΔOPS and ΔOQS

OS = OS (Common)

OP = OQ (Radius)

∠OSP = ∠OSQ

Therefore, ΔOPS ≅ ΔOQS (RHS criterion)

∠POS = ∠QOS (By C.P.C.T)

arc (PR) = arc (QR)

Thus, point R bisects the arc PRQ.