Circle C has radius 4 inches. Circle D had radius 9 inches. These two circles are connected. Point A,B,and E are points of tangency. Find AB. From point C to point D(which is the radius of circle C plus the raduis of circle D) it is 13 inches. From point C to point A (radius of circle C) it is 4 inches. From point D to point B it is 9 inches.(radius of circle D) What is the length from point A to point B? (if you connect the bottom of the two circles which point A is the point of tangency in circle C from the radius down forming a 90 degree angle and also point B is the point of tangency in circle D from the radius down forming a 90 degree angle)

Question

Thanks so much!

Answer 1

Where does point E enter the picture?
It is supposed to be a point of tangency, is it the point where the two circles are "connected" ?
It does not appear to enter into the calculation of AB.

From C draw a line parallel to AB to cut BD at F.
So FC = AB since we now have a rectangle where
angle DFC = 90°
by Pythagoras,
FC^2 + 5^2 = 13^2
FC = 12

so AB = 12