Question

A CHORD PQ OF A CIRCLE IS PARALLEL TO THE TANGENT DRAWN AT A POINT R OF THE CIRCLE. PROVE THAT R BISECTS THE ARC PRQ.

Answer 1

OR ⊥ m 

PQ || m given

∴∠OSP = ∠OSQ = 90° corresponding angles 

In ΔOPS and ΔOQS

OP = OQ (Radius)

OS = OS (Common)

∠OSP = ∠OSQ

So,ΔOPS ≅ ΔOQS (RHS criterion)

⇒ ∠POS = ∠QOS (By C.P.C.T)

⇒ arc (PR) = arc (QR)

Answer 2

Answer:

OR ⊥ m 

PQ || m given

∴∠OSP = ∠OSQ = 90° corresponding angles 

In ΔOPS and ΔOQS

OP = OQ (Radius)

OS = OS (Common)

∠OSP = ∠OSQ

So,ΔOPS ≅ ΔOQS (RHS criterion)

⇒ ∠POS = ∠QOS= Φ (By C.P.C.T)

By length of arc

Φ/360 x 2πr = Φ/360 x 2πr

⇒ arc (PR) = arc (QR)