What is the ratio $\frac{A C}{B C}$ for the following construction method?

1:2

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1:1

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Solution

The correct option is B
1:1

In the construction process given, triangles $△ A A_{12} B$ and $△ A A_{6} C$ are similar.

Hence, we get $\frac{A C}{A B} = \frac{6}{12} = \frac{1}{2}$

By construction $\frac{B C}{A B} = \frac{6}{12} = \frac{1}{2}$

$\frac{A C}{B C} = \frac{\frac{A C}{A B}}{\frac{B C}{A B}} = \frac{\frac{1}{2}}{\frac{1}{2}} = 1$

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What is the ratio ACBC for the following construction method?

The correct option is B 1:1 In the construction process given, triangles △AA12B and △AA6C are similar. Hence, we get ACAB=612=12 By construction BCAB=612=12 ACBC=ACABBCAB=1212=1

What is the ratio $\frac{A C}{B C}$ for the following construction method?