Skip to main content

15 replies

terryhendicott
terryhendicott21-Topaz II
21-Topaz II
Oct 12, 2025 6:42 AM UTC

Hi Fred,

I had some fun.

Have my answer in a closed area also to stop the honest among us who don't peek.

Cheers

Terry

Translate
ttokoro
ttokoro21-Topaz I
21-Topaz I
Oct 12, 2025 7:51 AM UTC

image.png

Translate
t.t.
    terryhendicott
    terryhendicott21-Topaz II
    21-Topaz II
    Oct 12, 2025 9:29 AM UTC

    Hi Fred,

    Remember this is fun.

    Intersection of perpendicular bisectors of AB and BD meet at the center.  Once have center can get radius center to A.

    Capture.JPG  

    Translate
      Werner_E
      Werner_E25-Diamond I
      25-Diamond I
      Oct 12, 2025 1:50 PM UTC

      As you posted a file in Prime Express 4.0 format, I thought I would provide an Express solution as well.
      Basically simply two perpendicular bisectors are intersected to get the center M of the circle and the radius is the distance of M to one of the three circle points A, B or D.

      Werner_E_0-1760276930700.png

      Prime Express 4 file attached

       

      Translate
        Werner_E
        Werner_E25-Diamond I
        25-Diamond I
        Oct 12, 2025 3:17 PM UTC

        Here a more basic approach without analytical geometry, just using good old Pythagoras.

        The solving of a system of equations (in r and MF) is somewhat hidden by  first expressing MF with r and putting that expression in the second equation.

        Werner_E_2-1760283108961.png

        "root" function can be avoided by some manual term manipulations

        Werner_E_3-1760283230867.png

        Prime Express 4 file attached

         

        Translate
          ppal_25568718-Opal
          18-Opal
          Oct 12, 2025 9:06 PM UTC

          Since this was for fun I thought I'd see if I could replace Mathcad with Gemini Ai.

          I have a circle. I draw a chord AB =45cm. Then I draw a line at 90 degrees to AB =20cm. This line is inside the circle. I draw another line perpendicular to  AC towards the circumference. This line is CD =15cm and terminates on the circumference of the circle. Determine the radius.

          ppal_6-1760303132747.png

           

          Translate
            StuartBruff23-Emerald V
            23-Emerald V
            Oct 12, 2025 11:20 PM UTC

            I was going to go Werner's "good old Pythagoras" route until I saw he'd already posted it.   So, as we've had Greeks, I'll go Indian instead.

             

            2025 13 09 A.png

            Translate
              ppal_25568718-Opal
              18-Opal
              Oct 12, 2025 11:28 PM UTC

              Well they are both Indian.

              The Baudhayana Shulba Sutra, an Indian text written between the 8th and 5th century BC, contains a statement of the theorem, a specific case for the isosceles right triangle, and the general case. This predates Pythagoras by about 300 years. 

              Translate
                AlanStevens19-Tanzanite
                19-Tanzanite
                Oct 15, 2025 12:25 PM UTC

                Here's another approach (Prime 11 Express):

                JUstForFun.png

                 

                Alan

                 

                Translate
                  Werner_E
                  Werner_E25-Diamond I
                  25-Diamond I
                  Oct 15, 2025 1:41 PM UTC

                  It's nice to see so many ways to skin this cat!

                   

                  > (There is probably a name for this relationship, but, if so, I've long forgotten it!)

                   

                  In German it's called "Höhensatz". According to Wikipedia its called "Geometric Mean Theorem" in English -> Geometric mean theorem - Wikipedia

                  Translate
                    Terms & ConditionsAccessibility statement