<p>In the diagram, \(AB\) is a diameter of the circle with centre \(O\). \(DE\) and \(BF\) are tangents to the circle at \(C\) and \(B\) respectively. \(DCE\) and \(BEF\) are straight lines. Prove that</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/1772958234844-izh3iqw8gv.png" style="max-width: min(400px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">\(\Delta ABC\) and \(\Delta BFC\) are similar,</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">hence or otherwise, show that&nbsp;\(\Delta CFE\) is an isosceles triangle.</span><span class="inline-marks">[4]</span></div></li></ol>

In the diagram, \(AB\) is a diameter of the circle with centre \(O\). \(DE\) and \(BF\) are tangents to the circle at \(C\) and \(B\) respectively. \(DCE\) and \(BEF\) are straight lines. Prove that

\(\Delta ABC\) and \(\Delta BFC\) are similar,

hence or otherwise, show that \(\Delta CFE\) is an isosceles triangle.

2025 AHS PRELIMS P1 Q13

2025 AHS PRELIMS P1 Q13