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<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>In the diagram, \(O\) is the centre of the circle with a radius of \(5\) cm and chord \(AB\) has a length of \(8\) cm.<br>Find</p><ol class="abc-list"><li><div class="list-item-paragraph">\(x\),</div></li><li><div class="list-item-paragraph">\(y\).</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1780570879316-s7rd72klp.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3ODA1NzA4NzkzMTYtczdyZDcya2xwLnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI3MjU1OTEsImV4cCI6MTc5MjcyNTg5MX0.WwlinU4yw3ltQwDj0pSN2jrlPGUHwV6Wk3hGxGzTKmU" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Applications of Pythagoras’ Theorem

Equal Chords and Distances from the Centre

Perpendicular Bisectors of Chords

Theoretical Principles of Circular Symmetry

Properties of Circle

Proofs in Plane Geometry

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>The figure below shows a circle with centre \(O\) and chords \(AB\) and \(CD\).<br>\(AB=5\) cm and \(OM=ON=3\) cm.<br>Calculate</p><ol class="abc-list"><li><div class="list-item-paragraph">the length of \(CN\).</div></li><li><div class="list-item-paragraph">the radius of the circle.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767596878608-znphqhb6v.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTY4Nzg2MDgtem5waHFoYjZ2LnBuZyIsInNjb3BlIjoiZG93bmxvYWQiLCJpYXQiOjE3OTI3MjU1OTEsImV4cCI6MTc5MjcyNTg5MX0.JvLxKhidv3dPbPzo6erhMiZt5sfYasx8-fCbFJV0DGA" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Symmetry and Right-Angled Triangles in Circles

<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><p>The figure shows a circle with centre \(O\).<br>\(AB=8\) cm and \(OM=ON=3\) cm.</p><ol class="abc-list"><li><div class="list-item-paragraph">Find the length of \(CN\).</div></li><li><div class="list-item-paragraph">Find the radius of the circle.</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure alignright" style="text-align: right;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767596200973-buj3wb30wzg.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTYyMDA5NzMtYnVqM3diMzB3emcucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcyNTU5MSwiZXhwIjoxNzkyNzI1ODkxfQ.D_FUorHLUNyOfKGuKFCZhefnBo1wACHzM8Ztj7PO2D4" style="max-width: min(180px, 100%); height: auto; display: block;" class="alignright custom-width" /></figure></div></div></div></div>

Symmetrical Properties of Chords in a Circle

<div class="content-block content-block--columns"><div class="question-columns question-columns--2-1" data-layout="2-1"><div class="question-column" style="flex: 2; align-self: flex-start;"><p>The diagram above is a circle with a centre \(O\), \(OX=5\) cm and \(AB=PQ=14\) cm.<br>\(OX\) is perpendicular to \(AB\) and \(OY\) is perpendicular to \(PQ\).<br>Find the length of</p><ol class="abc-list"><li><div class="list-item-paragraph">\(OY\),</div></li><li><div class="list-item-paragraph">\(YQ\).</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1767595339915-fa2u4mvm3dm.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3Njc1OTUzMzk5MTUtZmEydTRtdm0zZG0ucG5nIiwic2NvcGUiOiJkb3dubG9hZCIsImlhdCI6MTc5MjcyNTU5MSwiZXhwIjoxNzkyNzI1ODkxfQ.xWnah4-u2PlBChpGzm7snX1JqQgKX1cE7IYsNqF4STI" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div></div></div></div>

Applications of Circle Symmetric Property 2

Math Question Bank