2004 math CE

52)The centre of the circle is ( - 2/2 , - (-k)/2 ) = (- 1 , k/2)
x + y - 3 = 0 is a diameter of the circle since it divides the circle into two equal parts which is passing through the centre (- 1 , k/2).

So
- 1 + k/2 - 3 = 0
k = 8
Choose (D)
23)∠AEO + ∠ABD = 36° ( ext. ∠ of Δ )
∠AEO + (1/2)∠AOD = 36° (∠at centre twice ∠ at ☉ce)
∠AEO + (1/2)∠AEO = 36° (base ∠s, isos.Δ)
∠AEO = 24°
Choose (B)
18)△ABD : △CDE
= (△ABE + △BED) : △CDE
= ( (BE/CE)²△CDE + (BE/CE)△CDE ) : △CDE
= ( (1/3)² △CDE + (1/3)△CDE ) : △CDE
= (1/9 + 1/3) : 1
= 4 : 9
Choose (D)