{"id":639468,"date":"2023-06-26T06:21:53","date_gmt":"2023-06-26T00:51:53","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/find-the-length-of-the-tangent-from-an-external-point-p-at-a-distance-of-20-cm-from-the-centre-of-a-circle-of-radius-12-cm\/"},"modified":"2025-06-26T12:51:01","modified_gmt":"2025-06-26T07:21:01","slug":"find-the-length-of-the-tangent-from-an-external-point-p-at-a-distance-of-20-cm-from-the-centre-of-a-circle-of-radius-12-cm","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/find-the-length-of-the-tangent-from-an-external-point---p\/","title":{"rendered":"Find the length of the tangent from an external point P \u00a0 at a distance of 20\u00a0cm \u00a0 from the centre of a circle of radius 12 cm."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Find the length of the tangent from an external point P \u00a0 at a distance of 20\u00a0cm \u00a0 from the centre of a circle of radius 12 cm.","custom_permalink":"question\/mathematics\/find-the-length-of-the-tangent-from-an-external-point---p\/"},"categories":[],"acf":{"question":"

Find the length of the tangent from an external point<\/span>\r\n\r\n \r\n P<\/m:mi>\r\n <\/m:semantics><\/math>  at a distance of <\/span>\r\n\r\n \r\n \r\n 20<\/m:mn> <\/m:mo>cm<\/m:mtext><\/m:mrow>\r\n <\/m:semantics><\/math>  from the centre of a circle of radius 12 cm.<\/span><\/p>

\"10.<\/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":"    <\/span>14cm<\/span>","correct":false},{"option":"    <\/span>17cm<\/span>","correct":false},{"option":"    <\/span>16cm<\/span>","correct":true},{"option":"    <\/span>18cm<\/span> <\/span>","correct":false}],"solution":"Given that length of tangent is 20cm and radius of the circle is 12cm.<\/span>
\"10.We know that the tangents are perpendicular to the radius of the circle. <\/span>
Therefore, <\/span>\u2220<\/span>CDP = 90<\/span>\u00b0.<\/span>
In \u2206CDP, By Pythagoras theorem,<\/span>
\r\n\r\n \r\n \r\n \r\n \r\n \r\n (<\/m:mo>C<\/m:mi>D<\/m:mi>)<\/m:mo>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n +<\/m:mo>\r\n (<\/m:mo>P<\/m:mi>D<\/m:mi>)<\/m:mo>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n =<\/m:mo>\r\n (<\/m:mo>P<\/m:mi>C<\/m:mi>)<\/m:mo>\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 \u21d2<\/m:mo>\r\n (<\/m:mo>12<\/m:mn>)<\/m:mo>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n +<\/m:mo>\r\n (<\/m:mo>P<\/m:mi>D<\/m:mi>)<\/m:mo>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n =<\/m:mo>\r\n (<\/m:mo>20<\/m:mn>)<\/m:mo>\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 \u21d2<\/m:mo>\r\n (<\/m:mo>P<\/m:mi>D<\/m:mi>)<\/m:mo>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n =<\/m:mo>400<\/m:mn>\u2212<\/m:mo>144<\/m:mn>\r\n <\/m:mtd>\r\n <\/m:mtr>\r\n \r\n \r\n \u21d2<\/m:mo>\r\n (<\/m:mo>P<\/m:mi>D<\/m:mi>)<\/m:mo>\r\n 2<\/m:mn>\r\n <\/m:msup>\r\n =<\/m:mo>256<\/m:mn>\r\n <\/m:mtd>\r\n <\/m:mtr>\r\n \r\n \r\n \u21d2<\/m:mo>P<\/m:mi>D<\/m:mi>=<\/m:mo>16<\/m:mn>c<\/m:mi>m<\/m:mi>\r\n <\/m:mtd>\r\n <\/m:mtr>\r\n <\/m:mtable>\r\n \r\n <\/m:semantics><\/math> 
Hence, the length of the tangent from an external point P is 16cm.<\/span>
Therefore, option 3 is correct.<\/span>
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