Hi

I have two circle questions that I am a bit unsure of:

1.

Show that each of the circles with equations (x-3)² +(y-2)² = 25 and (x-2)² + (y-6)² = 25 passes through the centre of the other.

2.

The circle with centre Q has equation (x-5)² + (y-8)² = 9. PQR is a diameter of this circle parallel to the y-axis. The circles with centres P and R touch the circle with centre Q at R and P respectively. Find the equations of the larger circles.

EDIT:

Sorry, I've found another I can't do. I've managed to partially solve it, but am unable to complete.

In this sketch of a road roller, the diameter of the front wheel is half that of the rear wheel. The distance AB is 35 units. The equation of the rear wheel is (x-12)² + (y-13)² = 100. Find the equation AB and the equation of the front wheel.

Thank you in advance