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P25 [Geometry] - Turkish NMO 1st Round - 2014

Source:

May 26, 2014

geometry

Problem Statement

The circle

C_{1}

with radius

6

and the circle

C_{2}

with radius

8

are externally tangent to each other at

A

. The circle

C_3

which is externally tangent to

C_{1}

and

C_{2}

has a radius with length

21

. The common tangent of

C_{1}

and

C_{2}

which passes through

A

meets

C_{3}

at

B

and

C

. What is

|BC|

?

<span class='latex-bold'>(A)</span>\ 24 \qquad<span class='latex-bold'>(B)</span>\ 25 \qquad<span class='latex-bold'>(C)</span>\ 14\sqrt{3} \qquad<span class='latex-bold'>(D)</span>\ 24\sqrt{3} \qquad<span class='latex-bold'>(E)</span>\ 25\sqrt{3}

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