{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Circle Theorems - Part 1' data-url='/boclips/videos/634c049ef0c50125a1d07074' data-video-url='/boclips/videos/634c049ef0c50125a1d07074' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nCircle Theorems - Part 1\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30356647\" href=\"/search?publisher_ids%5B%5D=30356647\"\u003eFuseSchool\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eCREDITSAnimation \u0026amp; Design: Murray KnoxNarration: Lucy BillingsScript: Lucy BillingsIn these 3 videos we are going to discover 9 different circle theorems.I’m a big fan of them - they’re like little logic puzzles. Before we get...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eCREDITS\u003cbr/\u003eAnimation \u0026 Design: Murray Knox\u003cbr/\u003eNarration: Lucy Billings\u003cbr/\u003eScript: Lucy Billings\u003cbr/\u003e\u003cbr/\u003eIn these 3 videos we are going to discover 9 different circle theorems.\u003cbr/\u003e\u003cbr/\u003eI’m a big fan of them - they’re like little logic puzzles. Before we get started, you need to know what these words all mean.\u003cbr/\u003e\u003cbr/\u003eIf you aren’t sure, watch this video first.\u003cbr/\u003e\u003cbr/\u003eIn this first part, we’re going to look at 4 theorems inside the circle. And then in part 2 and 3 there will be lots of tangents and chords involved.\u003cbr/\u003e\u003cbr/\u003eLet’s get going. Here’s the first one…\u003cbr/\u003e\u003cbr/\u003eHopefully you can see that the angle at the centre is double the angle at the circumference.\u003cbr/\u003e\u003cbr/\u003eSometimes this theorem can be a little disguised…\u003cbr/\u003e\u003cbr/\u003eSee what happens when I move point B around…\u003cbr/\u003e\u003cbr/\u003eSo, if you see this sort of set-up… remember that the angle at the centre is double the angle at the circumference, even if it doesn’t have the normal “arrowhead” shape.\u003cbr/\u003e\u003cbr/\u003eHere’s theorem 2… we have a semi-circle.\u003cbr/\u003e\u003cbr/\u003eThe angle in a semi-circle is always 90 degrees. So that’s theorem 2.\u003cbr/\u003e\u003cbr/\u003eJust make sure that it really is a diameter - so it needs to cross through the centre.\u003cbr/\u003e\u003cbr/\u003eBy the way - the number doesn’t matter. Theorem 2 isn’t necessarily the semi-circle theorem. This is just the order we’re discovering them in this video.\u003cbr/\u003e\u003cbr/\u003eHere’s the next one.\u003cbr/\u003e\u003cbr/\u003eWe describe this one as “Angles in the same segment are equal”.\u003cbr/\u003e\u003cbr/\u003eSo, these angles are in the major segment.\u003cbr/\u003e\u003cbr/\u003eWe can also describe this theorem as angles subtended by the same arc are equal.\u003cbr/\u003eYou may like to remember of it as a bow tie shape, but you do need to use the key words… “segment” or “subtended by the same arc”. You choose which one you think is easier to remember.\u003cbr/\u003e\u003cbr/\u003eSo, we’re 3 theorems down. Here’s the last one for part 1…\u003cbr/\u003e\u003cbr/\u003eIt’s got 4 sides… so it must be a quadrilateral. But because it’s inside a circle and all 4 corners, or vertices, are touching the circumference we call it a cyclic quadrilateral.\u003cbr/\u003e\u003cbr/\u003eI’m sure you all spotted that the opposite angles add\u003cbr/\u003eup to 180 degrees. So that’s our fourth theorem...\u003cbr/\u003e\u003cbr/\u003eAnd the important part to remember is that all 4 sides must be touching the circumference for it to be a cyclic quadrilateral.\u003cbr/\u003e\u003cbr/\u003ePause the video, draw or write them all out making sure you use the correct descriptions.\u003cbr/\u003eSo, there are the first 4 theorems.\u003cbr/\u003e\u003cbr/\u003eWatch part 2 and 3 to discover another 5, that involve tangents and chords - and take us outside of the circle.\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='action-container flex justify-between'\u003e\n\u003cbutton aria-expanded='false' aria-label='Read more description' class='rp-full-description' type='button'\u003e\n\u003ci class='fai fa-solid fa-align-left'\u003e\u003c/i\u003e\n\u003cspan id='read_more'\u003eRead More\u003c/span\u003e\n\u003c/button\u003e\n\u003cdiv class='rp-report'\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='resource-details-heading' 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