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Home > CCG > Chapter 10 > Lesson 10.1.5 > Problem 10-54

10-54.

In the diagram at right, has radius feet and has radius feet. is tangent to both and . If feet, find .  

Two circles, left with center M, and radius, M, E, right with center A, and radius, A, r. Line E R is tangent to both circles, intersecting left circle at, E, and right circle at, r. Centers M and A are connected by a line segment which intersects left circle at, N, and right circle at, c. A dashed segment from, A, perpendicular to segment, M, E, at point, b.

Think about how the radius of will affect .
How will the radius of affect ?

After finding the lengths of  and , find lengths of the remaining sides.

 

because and and by the definition of a tangent.

Use Pythagorean Theorem to find the last side.

ft.