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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 5 · Set 2 · Q25
In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P. If ∠ QPT =55^°, then find ∠ PRQ.
In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P . If $\displaystyle \angle \mathrm{QPT}=55^{\circ}$, then find $\displaystyle \angle \mathrm{PRQ}$.
Marking-scheme solution
\[\begin{aligned}
& \angle \mathrm{QPT}=55^{\circ} \\
& \Rightarrow \angle \mathrm{OPQ}=90^{\circ}-55^{\circ}=35^{\circ} \\
& \Rightarrow \angle \mathrm{OQP}=35^{\circ} \\
& \angle \mathrm{POQ}=180^{\circ}-70^{\circ}=110^{\circ} \\
& \text { And reflex } \angle \mathrm{POQ}=250^{\circ} \\
& \text { Hence } \angle \mathrm{PRQ}=125^{\circ}
\end{aligned}
\]
This section comprises of short answer (SA) type questions of $\displaystyle 3$ marks each.
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.