# What is the radius of the circle?

## $A B = C D = 16$ $B C = D A = 8$

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

$10 \text{squares" xx (2units)/"square" = 20"units}$

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

consider the triangle $O A B$

from the diagram it can be seen that

$O A = r - 16$

$A B = r - 8$

we have aright angled triangle and so apply Pythagoras' theorem

${r}^{2} = {\left(r - 8\right)}^{2} + {\left(r - 16\right)}^{2}$

${r}^{2} = {r}^{2} - 16 r + 64 + {r}^{2} - 32 r + 256$

this simplifies to

${r}^{2} - 48 r + 320 = 0$

factorising

$\left(r - 40\right) \left(r - 8\right) = 0$

either

$r = 8$

this cannot be a solution as seen from the diagram

or

$r = 40$