The diagram shows a circle passing through the points $P$, $Q$, $R$ and $S$. Chord $SQ$ an

Question

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 triangle $RQU$ is isosceles.[3] Show that $\angle SPT = 2 \times \angle QPT$.[3]

Accepted Answer

(a) $QR=QU$, so $\triangle RQU$ is isosceles. (b) $\angle SPT=2\angle QPT$.

2025 SCGS PRELIMS P1 Q4

2025 SCGS PRELIMS P1 Q4

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