{"id":677009,"date":"2023-09-02T19:58:38","date_gmt":"2023-09-02T14:28:38","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/if-a-b-c-are-three-points-on-a-circle-with-center-o-such-that-%e2%88%a0aob90-and-%e2%88%a0boc120-then-what-will-be-the-measure-of-%e2%88%a0aoc\/"},"modified":"2025-06-26T13:11:35","modified_gmt":"2025-06-26T07:41:35","slug":"if-a-b-c-are-three-points-on-a-circle-with-center-o-such-that-%e2%88%a0aob90-and-%e2%88%a0boc120-then-what-will-be-the-measure-of-%e2%88%a0aoc","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-a-b-c-are-three-points-on-a-circle-with-center-o-such-t\/","title":{"rendered":"If A, B, C are three points on a circle with center O such that \u2220AOB=90\u00b0 and \u2220BOC=120\u00b0, then what will be the measure of \u2220AOC?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"If A, B, C are three points on a circle with center O such that \u2220AOB=90\u00b0 and \u2220BOC=120\u00b0, then what will be the measure of \u2220AOC?","custom_permalink":"question\/mathematics\/if-a-b-c-are-three-points-on-a-circle-with-center-o-such-t\/"},"categories":[],"acf":{"question":"

If A, B, C are three points on a circle with center O such that <\/span>\u2220<\/mo>AOB<\/mi>=<\/mo>90<\/mn>\u00b0<\/mo><\/math> and <\/span>\u2220<\/mo>BOC<\/mi>=<\/mo>120<\/mn>\u00b0<\/mo><\/math>, then what will be the measure of <\/span>\u2220<\/mo>AOC<\/mi><\/math>?<\/span><\/p>

<\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-left:0.1pt;margin-bottom:0pt;text-indent:-0.1pt;line-height:normal\">","options":[{"option":"60<\/mn>\u00b0<\/mo><\/math>","correct":false},{"option":"75<\/mn>\u00b0<\/mo><\/math>","correct":true},{"option":"90<\/mn>\u00b0<\/mo><\/math>","correct":false},{"option":"135<\/mn>\u00b0<\/mo><\/math> <\/span>","correct":false}],"solution":"Given, A, B, C are three points on a circle with center O such that <\/span>\u2220<\/mo>AOB<\/mi>=<\/mo>90<\/mn>\u00b0<\/mo><\/math>
and <\/span>\u2220<\/mo>BOC<\/mi>=<\/mo>120<\/mn>\u00b0<\/mo><\/math>.<\/span>
Construct a figure according to the given data,<\/span>
\"\"Here,<\/span>
\u2220<\/mo>AOC<\/mi>=<\/mo>360<\/mn>\u00b0<\/mo>-<\/mo>(<\/mo>120<\/mn>\u00b0<\/mo>+<\/mo>90<\/mn>\u00b0<\/mo>)<\/mo>=<\/mo>150<\/mn>\u00b0<\/mo><\/math>
But<\/span> <\/span>\u2220<\/span>AOC<\/span> <\/span>is at the center made by are AC and<\/span> <\/span>\u2220<\/span>ABC<\/span> <\/span>at the remaining part of the circle.<\/span>
Angle subtended by the arc at the center is double the angle subtended by it at any point on the circle.<\/span>
\u2220<\/mo>ABC<\/mi>=<\/mo>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac>\u2220<\/mo>AOC<\/mi><\/math>
=<\/mo>1<\/mn><\/mrow>2<\/mn><\/mrow><\/mfrac>\u00d7<\/mo>150<\/mn>\u00b0<\/mo><\/math>
=<\/mo>75<\/mn>\u00b0<\/mo><\/math>
Hence, the measure of <\/span>\u2220<\/span>AOC is <\/span>75<\/mn>\u00b0<\/mo><\/math>.<\/span>
Therefore, option 2 is correct.<\/span>
 <\/span>","subject":"Mathematics"},"yoast_head":"\nIf A, B, C are three points on a circle with center O such that \u2220AOB=90\u00b0 and \u2220BOC=120\u00b0, then what will be the measure of \u2220AOC? - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"If A, B, C are three points on a circle with center O such that \u2220AOB=90\u00b0 and \u2220BOC=120\u00b0, then what will be the measure of \u2220AOC?\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-a-b-c-are-three-points-on-a-circle-with-center-o-such-t\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If A, B, C are three points on a circle with center O such that \u2220AOB=90\u00b0 and \u2220BOC=120\u00b0, then what will be the measure of \u2220AOC? 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