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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
(b) One sapling is kept at point $P$ along $AB$ so that $PA = \frac{1}{3} PB$. Find the coordinates of $P$.
(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
(b) One sapling is kept at point $P$ along $AB$ so that $PA = \frac{1}{3} PB$. Find the coordinates of $P$.
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Solution:
(i) Coordinates of $O$ are $(12, 3)$
(ii) Radius $= 10$
(iii) (a) $OC = \text{radius} = 10$
$y = 13, y = -7$
Coordinates of the point 'C' are $(12, 13)$ or $(12, -7)$
OR
(iii) (b) $P$ divides $AB$ in the ratio $1 : 3$
Coordinates of $P$ are $\left( \frac{1 \times 22 + 3 \times 2}{4}, \frac{1 \times 3 + 3 \times 3}{4} \right)$
i.e. $(7, 3)$
(i) Coordinates of $O$ are $(12, 3)$
(ii) Radius $= 10$
(iii) (a) $OC = \text{radius} = 10$
$y = 13, y = -7$
Coordinates of the point 'C' are $(12, 13)$ or $(12, -7)$
OR
(iii) (b) $P$ divides $AB$ in the ratio $1 : 3$
Coordinates of $P$ are $\left( \frac{1 \times 22 + 3 \times 2}{4}, \frac{1 \times 3 + 3 \times 3}{4} \right)$
i.e. $(7, 3)$