Parallel-line angles

Scale factor lab

<p>In the diagram, \(TA\) and \(TB\) are tangents from \(T\) to the circle with centre \(O\) at \(A\) and \(B\), respectively. \(AC\) is a diameter of the circle. 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">angle \(AOB = 2 \times\) angle \(ACB\),</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">\(CB\) is parallel to \(OT\),</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">triangles \(OBC\) and \(TAB\) are similar, and</div></li><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">quadrilateral \(AOBT\) is a cyclic quadrilateral, i.e., there exists a circle that passes through \(A\), \(O\), \(B\) and \(T\).</div></li></ol>

In the diagram, \(TA\) and \(TB\) are tangents from \(T\) to the circle with centre \(O\) at \(A\) and \(B\), respectively. \(AC\) is a diameter of the circle. Prove that

triangles \(OBC\) and \(TAB\) are similar, and

quadrilateral \(AOBT\) is a cyclic quadrilateral, i.e., there exists a circle that passes through \(A\), \(O\), \(B\) and \(T\).

Proofs in Plane Geometry - Similarity

Proofs in Plane Geometry - Similarity

Video Solution:

Solution:

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