Euclidean Geometry Question 1

Question

$|FE| = 7 cm$

$|AB| = 2 cm$

OAEF is a rectangle. ABCD is a square.

O is the center of the quarter circle.

$|ED| = x =?$

Answer 1

Note that $OC,OE $ are radii of circle

By Pythagoras Theorem

$$(OB)^2+(BC)^2=r^2$$ where $r$ is radius of circle SO, $$r=\sqrt{85}$$

Similarly, $$(OF)^2+(FE)^2=r^2$$

$$(x+2)^2+49=r^2$$

which gives $x=4$