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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 3 · Set 1 · Q6
In Figure 2, PQ and PR are tangents to the circle centred at O. If ∠ OPR =45^°, then prove that ORPQ is a square. Figure 2
In Figure $\displaystyle 2$, PQ and PR are tangents to the circle centred at O . If $\displaystyle \angle \mathrm{OPR}=45^{\circ}$, then prove that ORPQ is a square.
Figure $\displaystyle 2$
Figure $\displaystyle 2$Marking-scheme solution
\[\begin{aligned}
& \triangle O Q P \cong \triangle O R P \Rightarrow \angle Q P O=\angle R P O=45^{\circ} \\
& \Rightarrow \angle Q P R=90^{\circ} . \text { Also } \angle O Q P=\angle O R P=\angle Q O R=90^{\circ}
\end{aligned}
\]
Also \(\displaystyle O R=O Q\). This implies \(\displaystyle O R P Q\) is a square.
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CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.