Problem 30 · 2010 Math Kangaroo
Stretch
Geometry & Measurement
spatial-reasoning
In the figure, \(\alpha = 7^\circ\). All the lines OA1, A1A2, A2A3, … are equally long. What is the maximum number of lines that can be drawn in this way if no two lines are allowed to intersect each other?
Show answer
Answer: D — 13
Show hints
Hint 1 of 2
Each equal segment makes an isosceles triangle, and the slope angle grows by 7° each step.
Still stuck? Show hint 2 →
Hint 2 of 2
The zigzag can continue only while that angle stays below 90°.
Show solution
Approach: track the growing angle
- With α = 7° and all segments equal, each new isosceles step increases the slope angle by 7°.
- The construction stays valid while the accumulated angle is under 90°: 7°×12 = 84° still works, but 7°×13 = 91° does not.
- Counting the segments that can still be drawn gives 13 lines.
Mark:
· log in to save