A circular table is placed in a corner of a room so that it touches both walls. A mark is made on the edge of the table that is exactly 18 inches from one wall and 25 inches from the other. What is the radius of the circular table?

Please and Thank you for helping!!!

SydSu22 Dec 5, 2018

#1**0 **

I come up with r=13

Since the circle sits agains both walls (the x and y axes), the center h,k is where x = y

the distance from the center to the point is the radius length and is also equal to the distance from the y axis to the center ...namely x equate these

sqrt [(x-25)^2 + (x-18)^2] = x square both sides

(x-25)^2 + (x-18)^2 = x^2

x^2 -50x+625 + x^2 -36x+324 = x^2

x^2-86x+949 = 0

Quadratic formula finds x = 73 or 13 73 is extraneous (too big) so x = 13

h,k then = 13,13 and radius = 13

(x-13)^2 + (y-13)^2 = 13^2 r= 13

Good point from Rom:

Both these answers are correct. If the radius is 73 in then the mark is to the right of the center of the circle. If the radius is 13 in then the mark is to the left of it. Although that would be a big table with ~ 12 foot diameter! But possible....

ElectricPavlov Dec 5, 2018

#3**+1 **

\(\text{Assume the corner is }(0,0)\\ \text{The equation of the table edge is }\\ (x+r)^2 + (y+r)^2 = r^2\\ \text{we are given that the point }(-18,-25) \text{ is on the table edge}\\ (-18+r)^2 + (-25+r)^2 = r^2\\ r^2 - 86r + 949 = 0\\ (r-73)(r-13) = 0\\ r=73 \text{ or }r=13\)

Both these answers are correct. If the radius is 73 in then the mark is to the right of the center of the circle. If the radius is 13 in then the mark is to the left of it.

Rom Dec 5, 2018