In the adjoining figure AC is diameter of a circle

1.	In the adjoining figure AC is diameter of a circle
Answer» Given: AC is the diameter of a circle whose centre is O. AB and CD are parallel chords of the circle.To prove : AB = CDConstruction: Draw OP {tex}\\perp{/tex}\xa0AB and OQ\xa0{tex}\\perp{/tex}\xa0CDProof : In {tex}\\triangle{/tex}s OAP and OQCOA = OC \|Radii of the same circle{tex}\\angle{/tex}OAB =\xa0{tex}\\angle{/tex}OCQ [Alt. {tex}\\angle{/tex}s]\xa0{tex}\\angle{/tex}OPA =\xa0{tex}\\angle{/tex}OQC [Each = 90o\xa0]\xa0{tex}\\therefore{/tex}\xa0{tex}\\triangle{/tex}OAP\xa0{tex}\\cong{/tex}\xa0{tex}\\triangle{/tex}OQC [AAS Axiom]{tex}\\therefore{/tex}\xa0OP = OQ [c.p.c.t]{tex}\\therefore{/tex}\xa0AB = CD[{tex}\\because{/tex}Chords of a circle which are equidistant from the centre are equal]

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