{"id":618420,"date":"2023-06-20T13:38:34","date_gmt":"2023-06-20T08:08:34","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/state-true-or-false-a-circle-has-radius-2-cm-it-is-divided-into-two-segments-by-a-chord-of-length-2-cm-then-angle-subtended-by-the-chord-at-a-point-in-the-major\/"},"modified":"2025-06-26T14:52:14","modified_gmt":"2025-06-26T09:22:14","slug":"state-true-or-false-a-circle-has-radius-2-cm-it-is-divided-into-two-segments-by-a-chord-of-length-2-cm-then-angle-subtended-by-the-chord-at-a-point-in-the-major","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/state-true-or-falsea-circle-has-radius-----------2--\/","title":{"rendered":"State true or false.A circle has radius 2 \u00a0\u00a0 cm. It is divided into two segments by a chord of length 2 cm. Then angle subtended by the chord at a point in the major segment is 55\u00ba."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"State true or false.A circle has radius 2 \u00a0\u00a0 cm. It is divided into two segments by a chord of length 2 cm. Then angle subtended by the chord at a point in the major segment is 55\u00ba.","custom_permalink":"question\/mathematics\/state-true-or-falsea-circle-has-radius-----------2--\/"},"categories":[],"acf":{"question":"

State true or false.<\/span><\/p>

A circle has radius <\/span>\r\n\r\n \r\n \r\n \r\n 2<\/m:mn>\r\n <\/m:msqrt>\r\n <\/m:mrow>\r\n <\/m:semantics><\/math>   <\/span>cm. It is divided into two segments by a chord of length 2 cm. Then angle subtended by the chord at a point in the major segment is 55\u00ba.<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:normal\">","options":[{"option":"True<\/span>","correct":false},{"option":"False<\/span> <\/span>","correct":true}],"solution":"Given that a circle has radius <\/span>\r\n\r\n \r\n \r\n \r\n 2<\/m:mn>\r\n <\/m:msqrt>\r\n <\/m:mrow>\r\n <\/m:semantics><\/math>   <\/span>cm. It is divided into two segments by a chord of length 2 cm. Then angle subtended by the chord at a point in the major segment is 55\u00ba.<\/span>
Creating figure using given data:<\/span>
\"\"We have<\/span>\r\n\r\n \r\n \r\n B<\/m:mi>C<\/m:mi>=<\/m:mo>2<\/m:mn><\/m:mrow>\r\n <\/m:semantics><\/math> .<\/span>
Now squaring on both sides of <\/span>\r\n\r\n \r\n \r\n B<\/m:mi>C<\/m:mi>=<\/m:mo>2<\/m:mn><\/m:mrow>\r\n <\/m:semantics><\/math> . <\/span>
\r\n\r\n \r\n \r\n \r\n \r\n \r\n \r\n \r\n B<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:mfenced>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n =<\/m:mo>\r\n 2<\/m:mn>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n \r\n <\/m:mtd>\r\n <\/m:mtr>\r\n \r\n \r\n \r\n \r\n \r\n B<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:mfenced>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n 4<\/m:mn>=<\/m:mo>2<\/m:mn>+<\/m:mo>2<\/m:mn>\r\n <\/m:mtd>\r\n <\/m:mtr>\r\n \r\n \r\n \r\n \r\n \r\n B<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:mfenced>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n =<\/m:mo>(<\/m:mo>\r\n \r\n 2<\/m:mn>\r\n )<\/m:mo>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n <\/m:mrow>\r\n <\/m:msqrt>\r\n +<\/m:mo>(<\/m:mo>\r\n \r\n 2<\/m:mn>\r\n )<\/m:mo>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n <\/m:mrow>\r\n <\/m:msqrt>\r\n \r\n <\/m:mtd>\r\n <\/m:mtr>\r\n <\/m:mtable>\r\n \r\n <\/m:semantics><\/math>  <\/span>\r\n\r\n \r\n \r\n \r\n \r\n \r\n \r\n B<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:mfenced><\/m:mrow>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n =<\/m:mo>\r\n \r\n \r\n \r\n O<\/m:mi>B<\/m:mi><\/m:mrow>\r\n <\/m:mfenced><\/m:mrow>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n +<\/m:mo>\r\n \r\n \r\n \r\n O<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:mfenced><\/m:mrow>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n <\/m:mrow>\r\n <\/m:semantics><\/math>  <\/span>So, in triangle BOC we have,<\/span>
\r\n\r\n \r\n \r\n \r\n \r\n \r\n \r\n B<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:mfenced><\/m:mrow>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n =<\/m:mo>\r\n \r\n \r\n \r\n O<\/m:mi>B<\/m:mi><\/m:mrow>\r\n <\/m:mfenced><\/m:mrow>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n +<\/m:mo>\r\n \r\n \r\n \r\n O<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:mfenced><\/m:mrow>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n <\/m:mrow>\r\n <\/m:semantics><\/math>  <\/span>Thus <\/span>\r\n\r\n \r\n \r\n \u2220<\/m:mo>B<\/m:mi>O<\/m:mi>C<\/m:mi>=<\/m:mo>\r\n \r\n 90<\/m:mn><\/m:mrow>\r\n \u00b0<\/m:mo>\r\n <\/m:msup>\r\n <\/m:mrow>\r\n <\/m:semantics><\/math>  (By Converse of Pythagoras theorem). <\/span>
So, <\/span>\r\n\r\n \r\n \r\n a<\/m:mi>r<\/m:mi>c<\/m:mi>B<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:semantics><\/math>  subtends <\/span>\r\n\r\n \r\n \r\n \u2220<\/m:mo>B<\/m:mi>O<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:semantics><\/math>  from the center O and angle <\/span>\r\n\r\n \r\n \r\n \u2220<\/m:mo>B<\/m:mi>A<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:semantics><\/math>  at left segment of the circle, <\/span>
Since the angle subtended by an arc at the center is double the angle subtended by it at any point on the left part of the circle, therefore<\/span>\r\n\r\n \r\n \r\n \u2220<\/m:mo>B<\/m:mi>O<\/m:mi>C<\/m:mi>=<\/m:mo>2<\/m:mn>\u2220<\/m:mo>B<\/m:mi>A<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:semantics><\/math> .<\/span>
\r\n\r\n \r\n \r\n \u2220<\/m:mo>B<\/m:mi>O<\/m:mi>C<\/m:mi>=<\/m:mo>2<\/m:mn>\u2220<\/m:mo>B<\/m:mi>A<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:semantics><\/math>  <\/span>\r\n\r\n \r\n \r\n \r\n \r\n 90<\/m:mn><\/m:mrow>\r\n \u00b0<\/m:mo>\r\n <\/m:msup>\r\n =<\/m:mo>2<\/m:mn>\u2220<\/m:mo>B<\/m:mi>A<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:semantics><\/math> 
\r\n\r\n \r\n \r\n \r\n \r\n \r\n \r\n 90<\/m:mn><\/m:mrow>\r\n \u00b0<\/m:mo>\r\n <\/m:msup>\r\n <\/m:mrow>\r\n 2<\/m:mn>\r\n <\/m:mfrac>\r\n =<\/m:mo>\u2220<\/m:mo>B<\/m:mi>A<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:semantics><\/math>  <\/span>\r\n\r\n \r\n \r\n \r\n \r\n 45<\/m:mn><\/m:mrow>\r\n \u00b0<\/m:mo>\r\n <\/m:msup>\r\n =<\/m:mo>\u2220<\/m:mo>B<\/m:mi>A<\/m:mi>C<\/m:mi><\/m:mrow>\r\n <\/m:semantics><\/math>  <\/span>\r\n\r\n \r\n \r\n \u2220<\/m:mo>B<\/m:mi>A<\/m:mi>C<\/m:mi>=<\/m:mo>\r\n \r\n 45<\/m:mn><\/m:mrow>\r\n \u00b0<\/m:mo>\r\n <\/m:msup>\r\n <\/m:mrow>\r\n <\/m:semantics><\/math>  <\/span>As the angle subtended by the chord at a point in major segment is <\/span>\r\n\r\n \r\n \r\n \r\n \r\n 45<\/m:mn><\/m:mrow>\r\n \u00b0<\/m:mo>\r\n <\/m:msup>\r\n <\/m:mrow>\r\n <\/m:semantics><\/math> , thus statement is false.<\/span>
Hence, option 2 is correct.<\/span>
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