✓ Board-verified↻ asked 2×
Mathematics · 2023 · 4 marks
CBSE 2023 · Region 1 · Set 1 · Q38
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 $\displaystyle \angle \mathrm{ABO}=30^{\circ} . \mathrm{PQ}$ 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 .
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 $\displaystyle \angle \mathrm{ABO}=30^{\circ} . \mathrm{PQ}$ 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)
$\displaystyle \sin 30^{\circ}=\frac{1}{2}=\frac{75}{O B}$
$\displaystyle \Rightarrow \mathrm{OB}=150 \mathrm{~cm}$
\[\begin{aligned}
\mathrm{QB} & =150-75=75 \mathrm{~cm} \\
& \Rightarrow \mathrm{Q} \text { is mid point. of } \mathrm{OB}
\end{aligned}
\]
Since PQ $\displaystyle 11$ AO therefore P is mid point of AB
Hence $\displaystyle \mathrm{AP}=\frac{75 \sqrt{3}}{2} \mathrm{~cm}$.
$\displaystyle \mathrm{QB}=150-75=75 \mathrm{~cm}$
Now, $\displaystyle \triangle \mathrm{BQP} \sim \triangle \mathrm{BOA}$
\[\begin{array}{l}
\Rightarrow \frac{Q B}{O B}=\frac{P Q}{O A} \\
\Rightarrow \frac{1}{2}=\frac{P Q}{75} \\
\Rightarrow P Q=\frac{75}{2} \mathrm{~cm}
\end{array}
\]
More from Circles
- Assertion: Radius is the smallest distance of a tangent from the centre of the circle. Reason (R): Radius is…2026 · asked 3×
- Assertion: The tangents drawn at the end points of a diameter of a circle, are parallel. Reason (R): Diameter…2024 · asked 3×
- Prove that the parallelogram circumscribing a circle is a rhombus.2024 · asked 3×
- A backyard is in the shape of a triangle ABC with right angle at B. AB=7 m and BC=15 m. A circular pit was…2024 · asked 3×
- PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at…2026 · asked 3×
- PQ is tangent to a circle with centre O. If ∠ POR=65^°, then m ∠ PTR is2026 · asked 3×
- Which of the following statements is false?2025 · asked 3×
- Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is:2024 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.