Parallel-line angles

<p>In the diagram, \(O\) is the centre of the smaller circle. \(ABC\) and \(AED\) are straight lines. Prove that</p>
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<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">\(AC = AD\), and</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">\(BE\) is parallel to \(CD\).</div></li></ol>
<p>As shown in the diagram, \(A,B,O,D\) lie on one circle, and \(B,C,D,E\) lie on the circle with centre \(O\).</p>

In the diagram, \(O\) is the centre of the smaller circle. \(ABC\) and \(AED\) are straight lines. Prove that

As shown in the diagram, \(A,B,O,D\) lie on one circle, and \(B,C,D,E\) lie on the circle with centre \(O\).

Basic Geometry - Angles Formed by Two Parallel Lines and a Transversal

Basic Geometry - Angles Formed by Two Parallel Lines and a Transversal

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Solution:

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