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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 \(H\).</p>
<p>Stating your reasons clearly, prove that</p>
<ol class="i-list"><li data-list-item-id="item-i"><div class="list-item-content"><span class="list-item-text">\(\Delta GFH\) and \(\Delta FEH\) are similar,</span><span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-1772953054553-i30rc3xba"><div class="list-item-paragraph">\(HF^2 =HE \times GH\)<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-1772953099586-5gwymv2ua"><div class="list-item-paragraph">\(AF^2 =AE^2 \times EF^2\)<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 \(H\).

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

2025 MGS PRELIMS P2 Q4

2025 MGS PRELIMS P2 Q4