Two identical touching circles of radius r share the same tangent. A square of side s, rests on the tangent and touches the two circles as shown in the diagram above. If r is 10 units. Then the side ss of the square is how many units?
+128460 See the following :
Let C =(-10,20) C = (0,0)
The slope of this line = -2
And the eqation of this line is y = -2x (1)
The equation of the circle with its ceenter at A is ( x+10)^2 + ( y - 10)^2 = 100 (2)
Sub (1) into (2) and we have that
(x + 10)^2 + ( -2x - 10)^2 = 100
x^2 + 20x + 100 + 4x^2 + 40x + 100 = 100
5x^2 + 60x + 100 = 0
x^2 + 12x + 20 = 0 factor as
( x + 10) ( x + 2) = 0
The second factor set to 0 and solved for x gives x = -2 = x coordinate of F
And the y coordinate is -2 (-2) = 4 = HF = side of the square
