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प्रश्न
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
विकल्प
True
False
उत्तर
This statement is True.
Explanation:
First, we draw a circle and a point from the given information
Now, distance between origin i.e., O(0, 0) and P(5, 0),
OP = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
OP = `sqrt((5 - 0)^2 + (0 - 0)^2`
= `sqrt(5^2 + 0^2)`
= 5
= Radius of circle and distance between origin O(0, 0) and Q(6, 8),
OQ = `sqrt((6 - 0)^2 + (8 - 0)^2`
= `sqrt(6^2 + 8^2)`
= `sqrt(36 + 64)`
= `sqrt(100)`
= 10
We know that, if the distance of any point from the centre is less than/equal to/more than the radius, then the point is inside/on/outside the circle, respectively.
Here, we see that, OQ > OP
Hence, it is true that point Q(6, 8), lies outside the circle.
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Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
Each team plays with 11 players on the field during the game including the goalie. Positions you might play include -
- Forward: As shown by players A, B, C and D.
- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
- Goalie: As shown by player K.
Using the picture of a hockey field below, answer the questions that follow:
If a player P needs to be at equal distances from A and G, such that A, P and G are in straight line, then position of P will be given by ______.
