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Understanding Circle Geometry: Properties, Chords, and Arcs Explained

Explore the intricate concepts of circle geometry, including essential properties like chords and arcs. This guide provides a detailed overview of how chords divide circles, the definition of minor and major arcs, and the relationships between various elements within a circle. With clear explanations and illustrations, readers will learn how to calculate the lengths of chords and the measures of angles pertaining to circles. Ideal for students and geometry enthusiasts, this resource simplifies complex ideas into digestible information.

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Understanding Circle Geometry: Properties, Chords, and Arcs Explained

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  1. c`kr pySkrqw : AMnUjYn srkwrIhweIskUlrwmpur luiDAwxw ivSw : ihswb jmwq : s`qvIN

  2. AwpxI kwpI qy ie`k ibMdU lgwE ijsdw nwm ‘o’ hY[ • ie~khoribMdU ‘p’ iesqrHWlgwEikausdIdUrI‘o’ qo3cmhovyijvyNikOP=3 cm O P   c`kr • AsI ies qrHW dy hor ikMny ibMdU lgw skdy hW[ au`qr : Axigxq • kIqusIiesqrHWdwkoeIhoribMdUlgwskdy ho ijsdIdUrI‘o’ qo 3cmhovy[ au`qr : hW [

  3. mMn lE AsI ies qrHW dy swry ibMdU jo ik ‘O’ qo 3 cm dI dUrI qy hn lgw ley qW swfy kol ie`k ic`qr iqAwr huMdw hY jo ik Q`ly idKweI dy irhw hY[  O P     • ie`h ic`qr nUM c`kr kihMdy hn[

  4. c`kr dw “kyNdr”Aqy“ArD ivAws” A B   • ie`sc`krv`liDAwnidE • ie`sc`krau`qycwribMdUl`gyhoeyhn A,B,C Aqy D [ • hr ibMdUnUM‘O’nwlimlwE. OA,OB,OC and OD dIdUrInUMiDAwnnwlmwpo[ • AsIdyKwgyNikswirAwdIdUrIbrwbrhY[ • c`krAijhyibMdUAWdwsumylhY, joikid`qygeyibMdUqobrwbrdIdUrIqyhn[ O    D C • id`qygeyibMdU ‘o’ nUM “c`krdwkyNdr”, AqydUrInUM “c`krdwArDivAws” kihMdyhn[

  5. c`kr dw ArD ivAws • AwE c`kr dyKIey ijsdw kyNdr ‘O’ hY[ • P,Q AqyR c`kr dy au`qy hn[. • jdo koeI lweIn c`kr dy kyNdr qo iksy ibMdU nUM imlweI jWdI hY qw ausnUM c`kr dw ArD ivAws kihMdy hn[ P  O   R  Q • ie`kc`krdyAxigxqArDivAws ho skdyhnijvyN OP,OQ,OR Awid[

  6. c`krdyAMdrUnIAqybwhrlyBwg • c`kr dy AMdr kox hY ? • ku`qw • c`kr dy bwhr kox hY ? • ib`lI Aqy gubwrw • syb c`kr dy iks pwsy hY[ • Syb c`kr dy au`qy siQ`q hY[

  7. c`kr dy AMdrUnI Aqy bwhrly Bwg • AwE dyKIey ibMdU A,B,C ik`Qy siQ`q hn[ • ‘A’ c`kr dy AMdr hY[ • ‘B’ c`kr au`qy siQ`q hY • ‘C’ c`kr dy bwhrly pwsy hY[ B  A    C

  8. jIvw (Chord of the Circle) B A • c`kr dy au`qy bxy do ibMdUAW nUM jdo ie`k lweIn bxw ik joiVAW jWdw hY qw ausnUM c`kr dI jIvw kihMdy hn[ • jdo jIvw c`kr dy kyNdr iv`co inkldI qW ausnUM c`kr dw ivAws kihMdy hn[ • jdo AsI jIvw dI dUrI mwpdy hW qw ivAws dI dUrI sB qo v`D huMdI hY[ C D P Q  F E G H • ie`k c`kr dIAW Axigxq jIvw huMdIAW hn[

  9. ivAws Aqy ArD ivAws iv`c sMbMD • ie`s ic`qr iv`c ‘O’ kyNdr qy AB ivAws hY[ • OA,OB ArD ivAws hn[ •  OA=OB Let OA=r, AB=d Then AB = OA+OB i.e. d = r+r = 2r O A B • • c`kr dw ivAws , ArD ivAws nwlo du`gxw huMdw hY[

  10. cwp(Arc of a Circle) • c`kr dy Coty ih`sy nUM cwp kihMdy hn, ijvyN ik c`kr iv`c motI gulwbI rMg iv`c drsweI geI hY[ies nUM cwp kihMdy hn[ • cwp jo ArD c`kr nwlo CotI huMdI hY aus nUM ‘Minor cwp’,Aqy bwkI ih`sy nUMMajor cwp kihMdy hn[ B A

  11. ArDc`kr • ie`k c`kr bxwE Aqy ausdw kyNdr ibMdU lgwE[ • ivAws ‘AB’ lweIn lgwE[ • c`kr nUM iesdy ivAws qo k`to[ • AsI dyKwgy ik c`kr dy ie`ko ijhy do ih`sy bx gey[ • iesdy dono Bwgw nUM ArD c`kr kihMdy hn[  B A

  12. KMf (Sector of a Circle) • AwE c`kr dyKIey[ • ‘O’ iesdw kyNdr Aqy OA,OB ArD ivAws hn[iesqo kox bxdw hYAOB. • kox AOB cwp AXB nUM k`tdw hY[ies qrRW dy bxy ic`qr nUM KMf kihMdy hn[ O  B A X

  13. c`kr dw Gyrw • c`kr dI lMbweI nUM c`kr dw Gyrw ikhw jWdw hY[ies nUM ‘C’ nwl drswieAw jWdw hY[

  14. ‘C’ Aqy ‘d’ iv`c sMbMD • v`Kry-v`Kry Akwr dy kuJ c`kr bxwE[ • Dwgy dI mdd nwl c`kr dw Gyrw Aqy c`kr dw ivAws mwpo[ • hr c`kr dy Gyry nUM ausdy ivAws nwl Bwg kro[

  15. ‘c’ Aqy ‘d’ iv`c sMbMD d S.No C C/d 7 22/7 1 22 14 22/7 2 44 66 21 22/7 3 88 28 4 22/7 110 35 22/7 5 • AsI dyKdy hW ik hr c`kr dI c/die`k smwn hY i.e. 22/7. • ies nUM grIk Sbd ‘’ (pweI) nwl iliKAw jWdw hY[ ies leI c`kr dw Gyrw iesdy ivAws nwlo pweI guxw huMdw hY[

  16. pRSnwvlI pRSn c`kr dy au`qy bxy do ibMdUAW nUM jdo ie`k lweIn bxw ik joiVAW jWdw hY qw ausnUM kI ikhw jWdw hY KMf jIvw

  17. jdo AsI jIvw dI dUrI mwpdy hW qw ivAws dI lMbweI bwkI jIvw nwlo ikMnI huMdI hY[ pRSnwvlI G`t v`D ip`Cy c`lo A`gy v`Do

  18. A`gy v`Do pRSnwvlI pRSn ie`k c`kr dy ikMny ArD ivAws ho skdy hn [ do Axigxq ip`Cy c`lo

  19. A`gy v`Do ip`Cy c`lo

  20. A`gy v`Do ip`Cy c`lo

  21. A`gy v`Do ip`Cy c`lo

  22. A`gy v`Do ip`Cy c`lo

  23. A`gy v`Do ip`Cy c`lo

  24. A`gy v`Do ip`Cy c`lo

  25. DMnvwd

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