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<p>The diagram shows two intersecting circles \(C_1\) and \(C_2\). The line \(CF\) intersects \(C_1\) at \(E\), and \(C_2\) at \(D\), such that&nbsp;\(CE = ED\). \(BAD\) is a straight line, where&nbsp;\(A\) is the centre of \(C_2\). The tangent to \(C_1\) at \(F\) meets \(EG\) produced at \(H\).<br>Stating your reasons clearly, prove that</p>
<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">\(\Delta GFH\) and \(\Delta FEH\) are similar,<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">\(HF^2 = HE \times GH\),<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-iii" data-list-item-path="item-iii"><div class="list-item-paragraph">\(AF^2 = AE^2 + EF^2\)<span class="inline-marks">[3]</span></div></li></ol>

The diagram shows two intersecting circles \(C_1\) and \(C_2\). The line \(CF\) intersects \(C_1\) at \(E\), and \(C_2\) at \(D\), such that \(CE = ED\). \(BAD\) is a straight line, where \(A\) is the centre of \(C_2\). The tangent to \(C_1\) at \(F\) meets \(EG\) produced at \(H\).
Stating your reasons clearly, prove that

\(\Delta GFH\) and \(\Delta FEH\) are similar,

Proofs in Plane Geometry

Proofs in Plane Geometry