{"id":358444,"date":"2023-01-07T01:44:46","date_gmt":"2023-01-06T20:14:46","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/choose-the-correct-optionthe-radius-of-a-circle-is-10-cm-and-the-length-of-one-of-its-chords-is-12-cm-find-the-distance-of-the-chord-from-the-centre\/"},"modified":"2025-06-26T12:44:39","modified_gmt":"2025-06-26T07:14:39","slug":"choose-the-correct-optionthe-radius-of-a-circle-is-10-cm-and-the-length-of-one-of-its-chords-is-12-cm-find-the-distance-of-the-chord-from-the-centre","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/choose-the-correct-optionthe-radius-of-a-circle-is-10-cm-an\/","title":{"rendered":"Choose the correct option:The radius of a circle is 10 cm and the length of one of its chords is 12 cm. Find the distance of the chord from the centre."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Choose the correct option:The radius of a circle is 10 cm and the length of one of its chords is 12 cm. Find the distance of the chord from the centre.","custom_permalink":"question\/mathematics\/choose-the-correct-optionthe-radius-of-a-circle-is-10-cm-an\/"},"categories":[],"acf":{"question":"<p>Choose the correct option:<\/p><p>The radius of a circle is 10 cm and the length of one of its chords is 12 cm. Find the distance of the chord from the centre.<\/p>","options":[{"option":"<p>6 cm<\/p>","correct":false},{"option":"<p>7 cm<\/p>","correct":false},{"option":"<p>8 cm<\/p>","correct":true},{"option":"<p>10 cm<\/p>","correct":false}],"solution":"<p>Let AB be a chord of a circle with centre O and radius 10 cm such that AB = 12 cm.<\/p><p>We draw OL \u22a5 AB and join OA.<\/p><figure class=\"image\"><img src=\"https:\/\/img-nm.mnimgs.com\/img\/study_content\/iit_pretests\/1\/9\/605\/3409\/\/16.2_html_3f3a9be0.png\"><\/figure><p><br>Since the perpendicular from the centre of a circle to a chord bisects the chord.<\/p><p>\u2234 AL = LB = AB\/2 = 6 cm<\/p><p>Now in \u25b3OAL, we have<\/p><p>OL<sup>2<\/sup> = OA<sup>2<\/sup> - AL<sup>2 &nbsp; &nbsp;<\/sup> &nbsp;[By Pythagoras theorem]<\/p><p>\u21d2 OL<sup>2<\/sup> = (10)<sup>2<\/sup> - (6)<sup>2<\/sup><\/p><p>\u21d2 OL<sup>2 <\/sup>= 100 - 36 = 64<\/p><p>\u21d2 OL = 8 cm<\/p><p>Hence the distance of the chord from the centre is <strong>8 cm<\/strong>.<\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Choose the correct option:The radius of a circle is 10 cm and the length of one of its chords is 12 cm. 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