SOLUTION: Let P be a point inside a square S so that the distances from P to the four vertices, in order, are 7, 35, 49, and x. What is x?

Question 636584: Let P be a point inside a square S so that the distances from P to the four vertices, in order, are 7, 35, 49, and x. What is x?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
636584
Let P be a point inside a square S so that the distances from P to the four vertices, in order, are 7, 35, 49, and x. What is x?
---------------
Make the square's vertices at (0,0), (0,s), (s,s) and (s,0)
The square is s by s units
-----
P is 7 units from (0,0), 35 units from (0,s) and 49 units from (s,s)
P is the intersection of 3 circles with the vertices as centers and the radii as given.
----------
The circles are:
x^2 + y^2 = 49
(x-s)^2 + y^2 = 1225
(x-s)^2 + (y-s)^2 = 2401
Solve for s
-------
(x-s)^2 + y^2 = 1225
(x-s)^2 + (y-s)^2 = 2401
--------------------------- Subtract
(y-s)^2 - y^2 = 1176
-2sy + s^2 = 1176
-------------
=============
x^2 + y^2 = 49
(x-s)^2 + y^2 = 1225
--------------------------- Subtract
x^2 - (x-s)^2 = - 1176
2sx - s^2 = -1176
s^2 - 2sx = 1176
------------------
==================
x^2 + y^2 = 49
(x-s)^2 + (y-s)^2 = 2401
--------------------------- Subtract
-2sx + s^2 - 2sy + s^2 = 2352
s^2 - sx - sy = 1176
===================================
I'll finish this later.
If you want to see it, email via the Thank You note.

RELATED QUESTIONS
P is any point inside a rectangle. Lines are drawn from P to the four vertices of the... (answered by greenestamps)

Let P be a point chosen uniformly at random inside triangle ABC. Extend ray BP to hit... (answered by CPhill,Edwin McCravy,ikleyn,mccravyedwin,AnlytcPhil,greenestamps,McCravyE,EPM)

Wanda is trying to locate the Fermat point P of triangle ABC, where A is at the origin, B (answered by Fombitz)

ABCD is a square with AB = 12. Point P is in an interior point whose distances to A, B,... (answered by checkley75)

7. Let q represent the number of widgets sold each week by a store, p represent the... (answered by math_tutor2020)

Four men and three women apply for a job at a company. three of the applicants are chosen (answered by stanbon)

points P(5,1), Q(0,6) and R(-5,1) are plotted on a coordinate plane. Where must point S... (answered by KMST)

Let P= (x,y) be a point on the graph on y=sqrt(x) or y=x^1/2 (not sure how to express... (answered by Fombitz)

Please help me with this!...I do not understand how to get the other answers without... (answered by stanbon)