What is the radius of the circle?

AB=CD=16AB=CD=16
BC=DA=8BC=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"10squares×2unitssquare=20units

Nov 12, 2017

r=40r=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 OABOAB

from the diagram it can be seen that

OA=r-16OA=r16

AB=r-8AB=r8

we have aright angled triangle and so apply Pythagoras' theorem

r^2=(r-8)^2+(r-16)^2r2=(r8)2+(r16)2

r^2=r^2-16r+64+r^2-32r+256r2=r216r+64+r232r+256

this simplifies to

r^2-48r+320=0r248r+320=0

factorising

(r-40)(r-8)=0(r40)(r8)=0

either

r=8r=8

this cannot be a solution as seen from the diagram

or

r=40r=40