Scale factor lab

<p>In the diagram, \(O\) is the centre of the circle, \(AC\) is a diameter and \(PAQ\) is the tangent to the circle at \(A\). 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">triangles \(CAP\) and \(CBA\) are similar, and</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">\(AC^2 = CP \times CB\).</div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">State a triangle that is similar to triangle \(CAQ\). Hence, or otherwise, prove that&nbsp;\(CP \times CB = CD \times CQ\).</div></li></ol>

In the diagram, \(O\) is the centre of the circle, \(AC\) is a diameter and \(PAQ\) is the tangent to the circle at \(A\). Prove that

triangles \(CAP\) and \(CBA\) are similar, and

State a triangle that is similar to triangle \(CAQ\). Hence, or otherwise, prove that \(CP \times CB = CD \times CQ\).

Proofs in Plane Geometry - Similarity

Proofs in Plane Geometry - Similarity

Video Solution:

Solution:

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