In the diagram, $O$ is the centre of the smaller circle passing through the points $P$, $S$, \

Question

In the diagram, $O$ is the centre of the smaller circle passing through the points $P$, $S$, $T$, $U$ and $R$. $QTR$ is a straight line. The points $P$, $Q$, $R$ and $O$ lie on the larger circle. It is given that angle $PQR=x^\circ$. Find angle $PSR$, in terms of $x$. Give a reason for each step of your working.[3] It is now given that angle $PUR$ is $105^\circ$. Find the value of $x$.[2]

Accepted Answer

(a) $90^\circ+\frac{x}{2}$ (b) $x=30$

2025 CGSS PRELIMS P1 Q19

2025 CGSS PRELIMS P1 Q19

Solution:

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