The diagram shows a circle with centre O and radius r cm. Points A and B lie on TU the circle and angle AOB = π/4 radians. The tangent to the circle at A intersects the straight line through O and B at the point C.

a) Find expressions in terms of r for

i) The area of sector OAB

ii) The length of AC

iii) The area of triangle OAC.

The area of the shaded region is 100 cm².

b) Find the value of r.

0 rcm TU 4 A B B C