Given: The radius of the circle is 1 unit Angle subtends by the chord at the center =2θ Concept Used: Sinθ= Perpendicular/Hypotenuse Calculation:
Construction: Draw a line OM⟂AB Now, In △AOM and △BOM OM=OM[ common side ] ∠AMO=∠BMO=90∘ And OA=OB [Hypotanuse of triangles] So, △AOM≅△BOM by R-H-S Rule of congruency So, ∠AOM=∠BOM=2θ∕2=θ And AM=BM=AB∕2 . . . (i) Now, In △BOM sinθ=BM∕OB=BM∕1 ⇒BM=sinθ Now, from (i), we get ⇒AB∕2=sinθ ⇒AB=2sinθ ∴ The length of chord is 2sinθ .