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]?

Result

x =  96

Solution:

r=(400)2+(300)2=50 x0=14=14  (x/2)2+x02=r2  x=2 r2x02=2 502142=96r=\sqrt{ (40-0)^2+(30-0)^2 }=50 \ \\ x_{0}=|-14|=14 \ \\ \ \\ (x/2)^2 +x_{0}^2=r^2 \ \\ \ \\ x=2 \cdot \ \sqrt{ r^2-x_{0}^2 }=2 \cdot \ \sqrt{ 50^2-14^2 }=96



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 

 

 

Next similar math problems:

  1. Two parallel chords
    chords_equall The two parallel chords of the circle have the same length of 6 cm and are 8 cm apart. Calculate the radius of the circle.
  2. Chord - TS v2
    chord_TS_1 The radius of circle k measures 87 cm. Chord GH = 22 cm. What is TS?
  3. Center
    circle Calculate the coordinates of the circle center: ?
  4. Equation of circle
    circle_analytics find an equation of the circle with indicated properties: a. center at (-3,5), diameter 20. b. center at origin and diameter 16.
  5. Circle - AG
    circle2 Find the coordinates of circle and its diameter if its equation is: ?
  6. A cell tower
    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?
  7. Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
  8. RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  9. Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  10. Distance
    distance Calculate distance between two points X[18; 19] and W[20; 3].
  11. RT triangle and height
    345 Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
  12. Segment
    segment_AB Calculate the length of the segment AB, if the coordinates of the end vertices are A[10, -4] and B[5, 5].
  13. Triangle IRT
    triangles_5 In isosceles right triangle ABC with right angle at vertex C is coordinates: A (-1, 2); C (-5, -2) Calculate the length of segment AB.
  14. Medians and sides
    3angle Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
  15. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  16. ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  17. Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.