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Mathematics · 2022 · 2 marks
CBSE 2022 · Region 2 · Set 1 · Q4
In Fig. $\displaystyle 1$, AB is diameter of a circle centered at O. BC is tangent to the circle at B . If OP bisects the chord AD and $\displaystyle \angle \mathrm{AOP}=60^{\circ}$, then find $\displaystyle \mathrm{m} \angle \mathrm{C}$.
Fig. $\displaystyle 1$In Fig. $\displaystyle 2$, XAY is a tangent to the circle centered at O. If $\displaystyle \angle \mathrm{ABO}=40^{\circ}$, then find $\displaystyle \mathrm{m} \angle \mathrm{BAY}$ and $\displaystyle \mathrm{m} \angle \mathrm{AOB}$. Fig.
In Fig. $\displaystyle 1$, AB is diameter of a circle centered at O. BC is tangent to the circle at B . If OP bisects the chord AD and $\displaystyle \angle \mathrm{AOP}=60^{\circ}$, then find $\displaystyle \mathrm{m} \angle \mathrm{C}$.
Fig. $\displaystyle 1$
In Fig. $\displaystyle 2$, XAY is a tangent to the circle centered at O. If $\displaystyle \angle \mathrm{ABO}=40^{\circ}$, then find $\displaystyle \mathrm{m} \angle \mathrm{BAY}$ and $\displaystyle \mathrm{m} \angle \mathrm{AOB}$. Fig.
Marking-scheme solution
\[\begin{array}{c}
\because A P=P D \Rightarrow O P \perp A D \\
\therefore \angle O A P=30^{\circ}
\end{array}
\]
Also $\displaystyle \angle A B C=90^{\circ}$
\[\Rightarrow \angle C=60^{\circ}
\]
Or
Fig. $\displaystyle 2$
\[\begin{array}{l}
O A=O B \Rightarrow \angle O A B=40^{\circ} \\
O A \perp A Y \Rightarrow \angle B A Y=50^{\circ} \\
\angle A O B=180^{\circ}-80^{\circ}=100^{\circ}
\end{array}
\]
Fig. $\displaystyle 2$
\[\begin{array}{l}
O A=O B \Rightarrow \angle O A B=40^{\circ} \\
O A \perp A Y \Rightarrow \angle B A Y=50^{\circ} \\
\angle A O B=180^{\circ}-80^{\circ}=100^{\circ}
\end{array}
\]More from Circles
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CBSE Class 10 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.