CPM Homework Help : INT2 Problem 10-94

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. In the diagram at right, $⊙M$ has a radius of $14$ feet and $⊙A$ has a radius of $8$ feet. $\overleftrightarrow { E R }$ is tangent to both $⊙M$ and $⊙A$ . If $NC = 17$ feet, what is $ER$ ?

Hint:

Use the given information to find the length of the hypotenuse of $ΔMBA$ .

Hint 2:

How can you use the radius of each circle to determine $MB$ ?

More Help:

Notice that the length of the dotted line is equivalent to $ER$ .

Answer:

$≈ 38.5 \; \text{feet}$