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Case Study - 2
There is a semicircular park in Aman's society. He wishes to plant saplings along the boundary of the park. There is a borewell at the centre $O$ of the park along the diameter $AB$ as shown in the figure below.
Based on the above information, answer the following questions :
(i) Find the coordinates of point $O$.
(ii) Find the radius of the semicircular park.
(iii) (a) One sapling is kept at point $C(12, y)$. Find the coordinates of $C$.
OR
(iii) (b) One sapling is kept at point $P$ along $AB$ so that $PA = \frac{1}{3} PB$. Find the coordinates of $P$.
There is a semicircular park in Aman's society. He wishes to plant saplings along the boundary of the park. There is a borewell at the centre $O$ of the park along the diameter $AB$ as shown in the figure below.
Based on the above information, answer the following questions :
(i) Find the coordinates of point $O$.
(ii) Find the radius of the semicircular park.
(iii) (a) One sapling is kept at point $C(12, y)$. Find the coordinates of $C$.
OR
(iii) (b) One sapling is kept at point $P$ along $AB$ so that $PA = \frac{1}{3} PB$. Find the coordinates of $P$.
Show SolutionHide Solution↓
(i) $\text{Coordinates of } O \text{ are } (12, 3)$ [$1$ mark]
(ii) $\text{Radius} = 10$ [$1$ mark]
(iii) (a) $OC = \text{radius} = 10$ [$\frac{1}{2}$ mark]
$y = 13, y = -7$ [$1$ mark]
$\text{Coordinates of the point 'C' are } (12, 13) \text{ or } (12, -7)$ [$\frac{1}{2}$ mark]
OR
(iii) (b) $P \text{ divides } AB \text{ in the ratio } 1 : 3$ [$\frac{1}{2}$ mark]
$\text{Coordinates of } P \text{ are } (\frac{1 \times 22 + 3 \times 2}{4}, \frac{1 \times 3 + 3 \times 3}{4})$ [$1$ mark]
$\text{i.e. } (7, 3)$ [$\frac{1}{2}$ mark]
(ii) $\text{Radius} = 10$ [$1$ mark]
(iii) (a) $OC = \text{radius} = 10$ [$\frac{1}{2}$ mark]
$y = 13, y = -7$ [$1$ mark]
$\text{Coordinates of the point 'C' are } (12, 13) \text{ or } (12, -7)$ [$\frac{1}{2}$ mark]
OR
(iii) (b) $P \text{ divides } AB \text{ in the ratio } 1 : 3$ [$\frac{1}{2}$ mark]
$\text{Coordinates of } P \text{ are } (\frac{1 \times 22 + 3 \times 2}{4}, \frac{1 \times 3 + 3 \times 3}{4})$ [$1$ mark]
$\text{i.e. } (7, 3)$ [$\frac{1}{2}$ mark]