Chord BC

A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]?

Correct answer:

x =  96

Step-by-step explanation:

$$\begin{gathered} r=\sqrt{(40-0{)}^2+(30-0{)}^2}=50 \\ {x}_0=\mathrm{\mid }-14\mathrm{\mid }=14 \\ (x\mathrm{/}2{)}^2+x_0^2=r^2 \\ x=2\cdot \sqrt{r^2-x_0^2}=2\cdot \sqrt{50^2-14^2}=96 \end{gathered}$$

Try another example

Related math problems and questions:

• Circle
  The circle touches two parallel lines p and q, and its center lies on line a, which is the secant of lines p and q. Write the equation of the circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
• A cell tower
  A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal?
• Square side
  Calculate length of side square ABCD with vertex A[0, 0] if diagonal BD lies on line p: -4x -5 =0.
• Center
  In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
• Vertices of a right triangle
  Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle.
• Right triangle from axes
  A line segment has its ends on the coordinate axes and forms with them a triangle of area equal to 36 square units. The segment passes through the point ( 5,2). What is the slope of the line segment?
• Coordinates hexagon
  The regular hexagon ABCDEF is given. Point A has coordinates [1; 3], and point D has coordinates [4; 7]. Calculate the sum of the coordinates of the center of its described circle.
• The triangle
  The triangle is given by three vertices: A [0.0] B [-4.2] C [-6.0] Calculate V (intersection of heights), T (center of gravity), O - center of a circle circumscribed
• Center
  Calculate the coordinates of the circle center: x² -4x + y² +10y +25 = 0
• Isosceles triangle
  In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C.
• On line
  On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
• Coordinates
  Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
• Center of line segment
  Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
• Find the 5
  Find the equation of the circle with center at (1,20), which touches the line 8x+5y-19=0
• Equation of circle 2
  Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x.
• Circle
  On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN.
• Two chords
  Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.