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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?

 

 Dec 23, 2020
 #1
avatar+117724 
-2

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  :

 

 

 

 

 

cool cool cool

 Dec 23, 2020
 #2
avatar+1164 
+3

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

 

 Dec 23, 2020
edited by jugoslav  Dec 24, 2020

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