<p>In the figure below, points \(A\), \(B\) and \(C\) lie on the circle. \(AC\) is a diameter of a circle with centre \(O\).</p>
<p>The tangent to the circle at \(X\) meets \(AC\) produced at \(Y\).</p>
<p>Chord \(XB\) intersects \(AC\) at \(F\).</p>
<p>\(XC\) bisects the angle of \(YXB\).</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1772876718073-pxts7acrugt.png" style="max-width: min(260px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li data-list-item-id="item-a"><div class="list-item-content"><span class="list-item-text">Prove that&nbsp;\(CX = CB\).</span><span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-1772876723177-qurajgz99"><div class="list-item-paragraph">Prove that triange AXC is similar to triangle BFC.<span class="inline-marks">[3]</span></div></li><li data-list-item-id="item-1772876757777-tycxkuufh"><div class="list-item-paragraph">Hence, prove that&nbsp;\(AC\times FC = BC^2\)<span class="inline-marks">[2]</span></div></li></ol>

In the figure below, points \(A\), \(B\) and \(C\) lie on the circle. \(AC\) is a diameter of a circle with centre \(O\).

The tangent to the circle at \(X\) meets \(AC\) produced at \(Y\).

Prove that triange AXC is similar to triangle BFC.

2025 CGSS PRELIMS P1 Q14

2025 CGSS PRELIMS P1 Q14