Question

# What is the ratio ACBC 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 A1,A2,...,A30 Step 2. A line is drawn from A30 to B and a line parallel to A30B is drawn, passing through the point A17 and meet AB at C.

A

17:30

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B

17:13

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C

13:17

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D

13:30

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Solution

## The correct option is B 17:13 Here the total number of arcs is equal to m+n in the ratio m:n. The triangles △ AA17C and △ AA30B are similar. Hence, ACAB = AA17AA30=1730 BCAB = AB−ACAB BCAB = 1 - 1730 = 1330 Hence, ACBC = 1713→17:13

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