2023 AMC 10 A

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Problem 22 Medium

Circles C _ { 1 } and C_{2} each have radius 1, and the distance between their centers is \frac { 1 } {2}. Circle C_{3} is the largest circle internally tangent to both C_{1} and C _ { 2 }. Circle C_{4} is intermally tangent to both C _ { 1 } and C _ { 2 } and externally tangent to C _ { 3 }. What is the radius of C_{4}?

  • A.

    \frac { 1 } {14}

  • B.

    \frac { 1 } {12}

  • C.

    \frac { 1 } {10}

  • D.

    \frac { 3 } {28}

  • E.

    \frac { 1 } {9}

Answer:C
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