Question

What is the ratio `(AC)/(BC)` 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.

विकल्प

• 13 : 30

• 13 : 17

• 17 : 13

• 17 : 30

Answer 1

17 : 13

Explanation:-

Here the total number of arcs is equal to m+n in the ratio m: n.

The triangles ΔAA₁₇C and ΔAA₃₀B are similar.

Hence, `(AC)/(AB)=(A A_17)/(A A_30) = 17/30`

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

`(BC)/(AB) = 1 - 17/30 = 13/30`

Hence, `(AC)/(BC) = 17/13 = 17:13`