<p>The diagram shows a circle passing through the points \(P\), \(Q\), \(R\) and \(S\). Chord \(SQ\) and \(RP\) intersect at \(T\). The straight line \(URV\) is a tangent to the circle at \(R\). The tangent meets the line \(SQ\) extended at \(U\) such that&nbsp;\(RU = RS\).</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/1772347180687-t77zl9fgt7.png" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Circle geometry diagram with points P, Q, R, S and tangent URV." class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Show that triangle \(RQU\) is isosceles.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Show that&nbsp;\(\angle SPT = 2 \times \angle QPT\).</span><span class="inline-marks">[3]</span></div></li></ol>

The diagram shows a circle passing through the points \(P\), \(Q\), \(R\) and \(S\). Chord \(SQ\) and \(RP\) intersect at \(T\). The straight line \(URV\) is a tangent to the circle at \(R\). The tangent meets the line \(SQ\) extended at \(U\) such that \(RU = RS\).

Show that \(\angle SPT = 2 \times \angle QPT\).

2025 SCGS PRELIMS P1 Q4

2025 SCGS PRELIMS P1 Q4