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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 1 · Set 3 · Q37
The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise around one and a half times through a…
The discus throw is an event in which an athlete attempts to throw a discus. The athlete spins anti-clockwise around one and a half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit.
In the given figure, AB is one such tangent to a circle of radius $\displaystyle 75$ cm . Point O is centre of the circle and $\displaystyle \angle \mathrm{ABO}=30^{\circ}$. PQ is parallel to OA.
Based on above information :
(a)
find the length of AB.
(b)
find the length of OB .
(c)
find the length of AP.
OR find the length of PQ .
Marking-scheme solution
(i)
\(\displaystyle \tan 30^{\circ}=\frac{1}{\sqrt{3}}=\frac{75}{\mathrm{AB}}\)
\(\displaystyle \Rightarrow \mathrm{AB}=75 \sqrt{3} \mathrm{~cm}\)
(ii)
\(\displaystyle \sin 30^{\circ}=\frac{1}{2}=\frac{75}{O B}\)
\(\displaystyle \Rightarrow \mathrm{OB}=150 \mathrm{~cm}\)
(iii)
\(\displaystyle \mathrm{QB}=150-75=75 \mathrm{~cm}\)
⇒ Q is mid- point. of OB
Since PQ ll AO therefore P is mid-point of AB
Hence \(\displaystyle \mathrm{AP}=\frac{75 \sqrt{3}}{2} \mathrm{~cm}\).
OR
(iii)
\(\displaystyle \mathrm{QB}=150-75=75 \mathrm{~cm}\)
Now, \(\displaystyle \Delta \mathrm{BQP} \sim \Delta \mathrm{BOA}\)
\[\Rightarrow \frac{Q B}{O B}=\frac{P Q}{O A}
\]
\[\begin{aligned}
& \Rightarrow \frac{1}{2}=\frac{P Q}{75} \\
& \Rightarrow P Q=\frac{75}{2} \mathrm{~cm}
\end{aligned}
\]
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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.