Scale factor lab

<p>In the diagram, the two circles touch each other externally at \(F\) and \(CFT\) is the common tangent. Given that&nbsp;\(ABC\), \(CDE\) and \(AFE\) 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">angle \(CBF + \text{angle}\hspace{0.5em} CDF = 180^\circ\), and</div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">angle \(BCD + \text{angle}\hspace{0.5em} BFD = 180^\circ\).</div></li><li data-list-item-id="item-1770117831518-ug1rdrv6i" data-list-item-path="item-1770117831518-ug1rdrv6i"><div class="list-item-paragraph">Hence prove that there exists a circle that passes through \(B\), \(C\), \(D\) and \(F\).</div></li></ol>
<p>Based on the answers above, or otherwise, prove that</p>
<ol class="i-list" start="4"><li data-list-item-id="item-iv" data-list-item-path="item-iv"><div class="list-item-paragraph">triangles \(BCD\) and \(ECA\) are similar, and</div></li><li data-list-item-id="item-v" data-list-item-path="item-v"><div class="list-item-paragraph">there exists a circle that passes through \(A\), \(B\), \(D\) and \(E\).</div></li></ol>

In the diagram, the two circles touch each other externally at \(F\) and \(CFT\) is the common tangent. Given that \(ABC\), \(CDE\) and \(AFE\) are straight lines, prove that

angle \(CBF + \text{angle } CDF = 180^\circ\), and

angle \(BCD + \text{angle } BFD = 180^\circ\).

Hence prove that there exists a circle that passes through \(B\), \(C\), \(D\) and \(F\).

Based on the answers above, or otherwise, prove that

triangles \(BCD\) and \(ECA\) are similar, and

there exists a circle that passes through \(A\), \(B\), \(D\) and \(E\).

Proofs in Plane Geometry - Alternate Segment Theorem

Proofs in Plane Geometry - Alternate Segment Theorem

Video Solution:

Solution:

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