Find the ratio AC/BC for the following construction method.
A ray AX is extended from A and 13 arcs of equal lengths are cut, cutting the ray at A1, A2… A13.
Another ray parallel to AX is extended from B and 2 arcs of equal lengths are cut, cutting the ray at B1 and B2. Line joining A13 and B2 cuts AB at C.

13:15

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13:2

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15:2

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None of these

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Solution

The correct option is B
13:2

In the construction process given, triangles $△ A A_{13} C$ and $△ B B_{2} C$ are similar.

So, $\frac{A C}{B C}$ = $\frac{A A_{13}}{B B_{5}}$

By construction, $\frac{A A_{13}}{B B_{5}}$ = $\frac{13}{2}$ .

Therefore, AC:BC= 13:2.

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Similar questions

Find the ratio AC:BC for the following construction method.
A ray AX is extended from A and 13 arcs of equal lengths are cut, cutting the ray at A1, A2… A13.
Another ray parallel to AX is extended from B and 2 arcs of equal lengths are cut, cutting the ray at B1 and B2. Line joining A13 and B2 cuts AB at C.

What is the ratio $\frac{A B}{B C}$ for the line segment AB following the construction method below?
Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_{1}, A_{2}, . . ., A_{30}$
Step 2. A line is drawn from $A_{30}$ to $B$ and a line parallel to $A_{30} B$ is drawn, passing through the point $A_{17}$ .

What is the ratio $\frac{A C}{B C}$ for the following construction method:
A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_{1}, A_{2} . . . . . . . A_{30}$ .
A line is drawn from $A_{30}$ to B and a line parallel to $A_{30} B$ is drawn, passing through the point $A_{17}$ .

What is the ratio $\frac{A C}{B C}$ for the line segment AB following the construction method below?
Step 1. A ray is extended from A and 30 arcs of equal lengths are cut, cutting the ray at $A_{1}, A_{2}, . . ., A_{30}$
Step 2. A line is drawn from $A_{30}$ to $B$ and a line parallel to $A_{30} B$ is drawn, passing through the point $A_{17}$ and meet AB at C.

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

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The correct option is B 13:2 In the construction process given, triangles △AA13C and △BB2C are similar. So, ACBC = AA13BB5 By construction, AA13BB5 = 132. Therefore, AC:BC= 13:2.

The correct option is B
13:2

In the construction process given, triangles $△ A A_{13} C$ and $△ B B_{2} C$ are similar.

So, $\frac{A C}{B C}$ = $\frac{A A_{13}}{B B_{5}}$

By construction, $\frac{A A_{13}}{B B_{5}}$ = $\frac{13}{2}$ .

Therefore, AC:BC= 13:2.