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.
Given Chord PQ is parallel to tangent at R.
To prove: R bisects the arc PRQ
Proof: ∠1 = ∠2 ....[Alternative interior angles]
∠1 = ∠3 ......[Angle between tangent and chord is equal to angle made by chord in alternative segment]
∴ ∠2 = ∠3
⇒ PR = QR ......[Sides opposite to equal angles are equal]
⇒ PR = QR
So, R bisects PQ.
Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
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