The chord of a circle divides the circle into two parts. A square of area 16 is inscribed in one part, and a square of area 144 is inscribed in the other part. The radius of the cirlce is?
+129907 The smaller square cannot be totally enclosed in the circle
To see why :
A right angle of the square will have its endpoints on the diameter of the circle = the diagonal of the square = 12sqrt (2)
So....the radius = 6sqrt (2) ≈ 8.48 units
But the center of the square = the center of the circle
So....the total combined length of (1/2) side length of larger square + side of smaller square = 6 + 4 =10 units
But this is larger than the radius of the circle....so.......the small square is not totally contained in the circle
See the pic here :
+1641 The chord of a circle divides the circle into two parts. A square of area 16 is inscribed in one part, and a square of area 144 is inscribed in the other part. The radius of the circle is?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Note that only 2 vertices of each square are on the circle!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
∠CBR = ∠PQO = tan-1(CR / BR) ==> 14.03624347º
P and Q are midpoints on TS and BC
CQ = 1/2 * sqrt(CR2 + BR2) = √68
PQ = 1/4(AB + CD) = 4
OQ = PQ / cos∠PQO = √17
CO = r = sqrt(OQ2 + CQ2) ==> r = √85
