Need help (vectors and circle geometry)!

Vectors- i and j are unit vectors- i=1 unit along the x axis j=1 unit along the y axis.

1. Given that a= 2i+3j

Find the angle it makes with the positive x axis.

2. Given that a=i + j and b= 2i - j

Find the angle each makes with the positive x axis a) 2a+b and b) 3b-a

3. A chord of a circle (x+2)^2+(y-9)^2=26 has the equation y=x+5.

Find the coordinates of the end points of the chord and hence find the equation of the perpendicular bisector of the chord. Verify that the perpendicular bisector passes through the centre of the circle.

4. The points A(1,5) and B (7,9) are the ends of a diameter of circle. Show that P (2,4) lies on the circle by showing that AP and BP are perpendicular and using the property that the angle in a semicircle is a right angle.

for question 4 I found that AP and BP are perpendicular after substituting the values of A, P and B (gradients are 1 and -1) however what else do I need to prove?

Thanks so much in advance if you can help :)