Not a coffee maker

- Do you know what I got for my birthday from my wife?
- A coffee maker?
- Nope. Three line segments that measured 1, a, and b.
- How thoughtful of her. I guess you didn’t have them already.
- You are right. It made me extremely happy.
- How long did the happiness last?
- Till the next morning.
- What happened then?
- She asked me to make a line segment which measured a times b.
- I would have preferred the coffee maker.

Problem source: Pandalous.

9 Responses to “Not a coffee maker”

  1. Richard Sabey Says:

    Draw two intersecting lines L, M at random. Let them intersect at A. On line L construct B and C on opposite sides of A such that AB = a and AC = b. On line M construct D such that AD = 1. Construct the circle that goes through B, C and D. It intersects M at E where AE = ab.

    To construct the circle: construct the perpendicular bisectors of the line segments BC and CD. These intersect at O, the centre of the circle. The circle’s radius is OB.

    Intersecting Chords theorem

  2. Adam Says:

    @ Richard – thanks. lol – Can’t we just have the coffee instead?

    - Adam

  3. Jill Says:

    ha ha – kind of reminds me of René Magritte painting if a pipe with the inscription “This Is Not A Pipe” - Jill Copper

  4. Daniel Says:

    Who says the pyramids were built by extraterrestrials? Richard, I never would have thought of that…but I do follow your instructions of the theorem quite clearly.

    I’m sure, also, that you have forgotten more geometry than I will ever remember.

    Well done, sir.

  5. Anceps Says:

    It can be done quicklier using Thales’ Intercept Theorem:


    A- – - -E- -C

    If AD is 1, AB is b and AE is a,
    then, AC is ab!

    Using the Intersecting Chord Theorem would be far better for this problem:
    Given a segment of length 1 and another segment s, find a segment of length that is the square root of s.
    (Which is the same as using the right triangle altitude formula* and Thales’ Circle Theorem)

    *In a right triangle, the altitude with the hypotenuse as base divides the hypotenuse into two lengths p and q. If we denote the length of the altitude by h, we then have the relation h^2 = pq.

  6. Jesse Jelley Says:

    Wow, okay, you all went totally over my head! I guess I don’t remember my geometry from junior high. LOL! Either way, love coffee, not necessarily this machine. I def. drink too coffee to do one cup at a time. :)

  7. Jim Says:

    Well that formula would certainly give me a headache if I could not have my coffee first. Maybe you will get lucky on next years birthday!

  8. Truck Bodies Says:

    Why was this coffee machine worth mentioning in the first place? lol. I guess that’s just something you expected but, if she is the type of woman who does this instead…i just dont see the connection. Interesting story though.

  9. Brett Says:

    lol. a lot of these replays are hilarious!!

    Not a coffee machine? Well they tricked me :)

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