What is the radius of the circle?

#AB=CD=16#
#BC=DA=8#
enter image source here

2 Answers
Nov 9, 2017

4 squares = 16 units; therefore 1 square = 2 units

There diameter of the circle is 20 squares. There for the radius of the circle is 10 squares

#10"squares" xx (2units)/"square" = 20"units"#

Nov 12, 2017

#r=40#

Explanation:

note some of the simplification is omitted and is left for the reader to verify.

consider the upper left hand quadrant

enter image source here

consider the triangle #OAB#

from the diagram it can be seen that

#OA=r-16#

#AB=r-8#

we have aright angled triangle and so apply Pythagoras' theorem

#r^2=(r-8)^2+(r-16)^2#

#r^2=r^2-16r+64+r^2-32r+256#

this simplifies to

#r^2-48r+320=0#

factorising

#(r-40)(r-8)=0#

either

#r=8#

this cannot be a solution as seen from the diagram

or

# r=40#