The diagram shows tangent circles and lines. if AB=15 CM find AC, AD and AE .

Help me reiny and other tutors please<3 thank you

this is the figure img19.(imageshack.)us/img19/7143/0eua.png

just remove the open and close parentheses thank you

This is just too easy.

Remember that both tangents to the same circle from an exterior point are equal.
so AB = AC
but AC is also tangent to the small circle
so AC = AD
but AD is also a tangent to the circle at the right
so AD = AE

Since the are all equal , and AB = 15
each one of them is 15

To find AC, AD, and AE, let's analyze the given diagram step by step.

Step 1: Identify the given information:
- AB = 15 cm

Step 2: Understand the properties of tangent circles and lines:
- The point where a line intersects a circle is called a point of tangency.
- When a line is tangent to a circle, it forms a right angle with the radius drawn to the point of tangency.

Step 3: Analyze the diagram:
Looking at the diagram, we can see that AB is the common tangent for both circles. This means that AB is perpendicular to the radii drawn from the center of each circle to the point of tangency.

Step 4: Determine the radius of the circles:
Since AB is perpendicular to the radii, this means that the line AB bisects the centers of both circles.
- The distance from the point of tangency to the center of a circle is equal to the radius of that circle.

Step 5: Calculate the radius of the circles:
Since AB bisects the centers of both circles, it means that the centers of the circles and the points of tangency form a right triangle.
- Let O1 and O2 be the centers of the circles, and let T1 and T2 be the points of tangency for the circles.
- The length of OT1 and OT2 is equal to the radius of each corresponding circle.

Step 6: Determine the lengths of OT1 and OT2:
Since AB is perpendicular to the radii, the triangle formed by O1, T1, and B is a right triangle.
- Using the Pythagorean theorem, we can find the length of OT1:
OT1^2 = OB^2 - BT1^2

Step 7: Apply the Pythagorean theorem to find OT1:
In the right triangle O1TB, OT1 is the hypotenuse, OB is the adjacent side, and BT1 is the opposite side.
- We know that BT1 = AB/2 = 15/2 = 7.5 cm (since AB is bisecting O1)
- To find OB, we can use the fact that O1B is perpendicular to AB, and therefore O1B is the height of right triangle O1TB.
- OB is the radius of the larger circle, which we can call r1.
- Therefore, OT1^2 = r1^2 - (7.5)^2

Step 8: Calculate the value of OT1:
We need the value of r1 to solve for OT1 completely. Unfortunately, the diagram does not provide any information about the radius of the larger circle.

Step 9: Repeat steps 6-8 for OT2:
We need the value of r2, the radius of the smaller circle, to calculate OT2. Unfortunately, this information is also missing from the provided diagram.

Conclusion:
Without the information about the radii of the circles, we cannot determine the values of AC, AD, and AE.