Advertisements
Advertisements
प्रश्न
If the point A (4,3) and B ( x,5) lies on a circle with the centre o (2,3) . Find the value of x.
Advertisements
उत्तर
Given, the points A(4,3) and B(x,5) lie on a circle with center o(2,3) . Then OA = OB
Also `(OA)^2 = (OB)^2`
`⇒(4-2)^2 + (3-3)^2 = (x-2) ^2 +(5-3)^2`
`⇒(2)^2+(0)^2=(x-2)^2 +(2)^2`
`⇒ 4=(x-2)^2 +4`
`⇒(x-2)^2 =0`
⇒ x -2 = 0
⇒ x =2
Therefore, x= 2
APPEARS IN
संबंधित प्रश्न
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.
The points (3, -4) and (-6, 2) are the extremities of a diagonal of a parallelogram. If the third vertex is (-1, -3). Find the coordinates of the fourth vertex.
If the poin A(0,2) is equidistant form the points B (3, p) and C (p ,5) find the value of p. Also, find the length of AB.
Show that the points A(6,1), B(8,2), C(9,4) and D(7,3) are the vertices of a rhombus. Find its area.
Show that the points A(2,1), B(5,2), C(6,4) and D(3,3) are the angular points of a parallelogram. Is this figure a rectangle?
Find the coordinates of the points of trisection of the line segment joining the points (3, –2) and (–3, –4) ?
Find the possible pairs of coordinates of the fourth vertex D of the parallelogram, if three of its vertices are A(5, 6), B(1, –2) and C(3, –2).
A point whose abscissa is −3 and ordinate 2 lies in
If the points P, Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B(7, 10) in 5 equal parts, find x, y and p.
Points P, Q, R and S divides the line segment joining A(1, 2) and B(6, 7) in 5 equal parts. Find the coordinates of the points P, Q and R.
If the point \[C \left( - 1, 2 \right)\] divides internally the line segment joining the points A (2, 5) and B( x, y ) in the ratio 3 : 4 , find the value of x2 + y2 .
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
If the points A (1,2) , O (0,0) and C (a,b) are collinear , then find a : b.
If (x , 2), (−3, −4) and (7, −5) are collinear, then x =
The ratio in which the line segment joining points A (a1, b1) and B (a2, b2) is divided by y-axis is
The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
The distance of the point P(2, 3) from the x-axis is ______.
(–1, 7) is a point in the II quadrant.
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So, he started to sketch his own rocket designs on the graph sheet. One such design is given below :
Based on the above, answer the following questions:
i. Find the mid-point of the segment joining F and G. (1)
ii. a. What is the distance between the points A and C? (2)
OR
b. Find the coordinates of the points which divides the line segment joining the points A and B in the ratio 1 : 3 internally. (2)
iii. What are the coordinates of the point D? (1)
