AMC 10 Daily Practice - Tangency

Complete problem set with solutions and individual problem pages

Problem 2 Easy

As shown in the figure, the diameter of each circle is 8\text{cm}. Therefore, the value of "?" is            \text{cm}.

  • A.

    4 ( 1 + 2 \sqrt { 3 } )

  • B.

    4 ( 2 + \sqrt { 3 } )

  • C.

    24

  • D.

    8 ( 1 + \sqrt { 3 } )

  • E.

    8 ( 2 + \sqrt { 3 } )

Answer:D

First, form a equilateral triangle ：

​​

Diameter is 8 cm, thus length of triangle is 16 cm.

Then divide the triangle through the top vertex.

Apply the Pythagorean Theorem c^2 = a^2 + b^2, to calculate the height of the triangle,

256 = 64 + h^2, h = 8\sqrt{3}

Add the miss part from the top and bottom,

? = 4(2) + 8\sqrt{3}

? = 8 + 8\sqrt{3} = 8(1 + \sqrt{3})

Thus, the answer is D.

Related Problems
Problem 1 AMC 10 Daily Practice - Tangency
Problem 3 AMC 10 Daily Practice - Tangency
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