Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
In what ratio is the line segment joining (-3, -1) and (-8, -9) divided at the point (-5, -21/5)?
Prove that the points (4, 5) (7, 6), (6, 3) (3, 2) are the vertices of a parallelogram. Is it a rectangle.
If the points A (a, -11), B (5, b), C (2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, −3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.
Find the area of quadrilateral ABCD whose vertices are A(-5, 7), B(-4, -5) C(-1,-6) and D(4,5)
If the points A (2,3), B (4,k ) and C (6,-3) are collinear, find the value of k.
If the point P (m, 3) lies on the line segment joining the points \[A\left( - \frac{2}{5}, 6 \right)\] and B (2, 8), find the value of m.
Find the value of k, if the points A (8, 1) B(3, −4) and C(2, k) are collinear.
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.
Write the ratio in which the line segment joining points (2, 3) and (3, −2) is divided by X axis.
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
If points Q and reflections of point P (−3, 4) in X and Y axes respectively, what is QR?
If the area of the triangle formed by the points (x, 2x), (−2, 6) and (3, 1) is 5 square units , then x =
If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is
The ratio in which the line segment joining P (x1, y1) and Q (x2, y2) is divided by x-axis is
If the sum of X-coordinates of the vertices of a triangle is 12 and the sum of Y-coordinates is 9, then the coordinates of centroid are ______
Write the X-coordinate and Y-coordinate of point P(– 5, 4)
The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are ______.
In which quadrant, does the abscissa, and ordinate of a point have the same sign?
If the vertices of a parallelogram PQRS taken in order are P(3, 4), Q(–2, 3) and R(–3, –2), then the coordinates of its fourth vertex S are ______.
