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प्रश्न
If the points A(4,3) and B( x,5) lie on the circle with center O(2,3 ) find the value of x .
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उत्तर
The given points A(4, 3) and B(x, 5) lie on the circle with center O(2, 3). Then, OA = OB
`⇒ sqrt((x-2)^2 +(5-3)^2) = sqrt((4-2)^2 +(3-3)^2)`
`⇒ (x-2)^2 +2^2 =2^2+0^2`
`⇒ (x-2)^2 = (2^2 -2^2)`
`⇒ (x-2)^2=0`
⇒ x - 2 = 0
⇒ x = 2
Hence, the value of x = 2
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संबंधित प्रश्न
(Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.
All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines.
There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:
- how many cross - streets can be referred to as (4, 3).
- how many cross - streets can be referred to as (3, 4).
Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.
Prove that the points (0, 0), (5, 5) and (-5, 5) are the vertices of a right isosceles triangle.
Name the quadrilateral formed, if any, by the following points, and given reasons for your answers:
A(-3, 5) B(3, 1), C (0, 3), D(-1, -4)
Prove that (4, 3), (6, 4) (5, 6) and (3, 5) are the angular points of a square.
If p(x , y) is point equidistant from the points A(6, -1) and B(2,3) A , show that x – y = 3
If the point P (2,2) is equidistant from the points A ( -2,K ) and B( -2K , -3) , find k. Also, find the length of AP.
Find the ratio in which the point (−3, k) divides the line-segment joining the points (−5, −4) and (−2, 3). Also find the value of k ?
Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.
Mark the correct alternative in each of the following:
The point of intersect of the coordinate axes is
The area of the triangle formed by the points A(2,0) B(6,0) and C(4,6) is
Find the centroid of the triangle whose vertices is (−2, 3) (2, −1) (4, 0) .
If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.
If the points A(−2, 1), B(a, b) and C(4, −1) ae collinear and a − b = 1, find the values of aand b.
If points Q and reflections of point P (−3, 4) in X and Y axes respectively, what is QR?
A line intersects the y-axis and x-axis at P and Q , respectively. If (2,-5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.
Point (–3, 5) lies in the ______.
If the coordinate of point A on the number line is –1 and that of point B is 6, then find d(A, B).
The distance of the point (–1, 7) from x-axis is ______.
