What is the ratio $\frac{A C}{B C}$ for the following construction method:
A line segment AB is drawn.
A single ray is extended from A and 12 arcs of equal lengths are cut, cutting the ray at $A_{1}$ , $A_{2}$ … $A_{12}$ .
A line is drawn from $A_{12}$ to B and a line parallel to $A_{12}$ B is drawn, passing through the point $A_{6}$ and cutting AB at C

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 $△ A A_{12} B$ $△ A A_{6} C$ are similar.

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

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

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

= $\frac{\frac{1}{2}}{\frac{1}{2}}$ = 1.

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Similar questions

What is the ratio $\frac{A C}{B C}$ for the following construction:
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A line is drawn from $A_{12}$ to B and a line parallel to $A_{12} B$ is drawn, passing through the point $A_{6}$ and cutting AB at C.

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