Question

What is the ratio `(AC)/(BC)` for the following construction: 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 A1, A2… A12.A line is drawn from A12 to B and a line parallel to A12B is drawn, passing through the point A6 and cutting AB at C.

Options

• 1 : 2

• 1 : 1

• 2 : 1

• 3 : 1

Answer 1

1 : 1

Explanation:-

In the construction process given,

triangles ΔAA₁₂B ΔAA₆C are similar.

Hence, we get `(AC)/(AB) = 6/12 = 1/2`

By construction `(BC)/(AB) = 6/12 = 1/2`

`(AC)/(BC) = (AC)/(AB)/ (BC)/(AB)`

`(1/2)/(1/2)=1`