Ma-POW #1

Over the break, I started making a headboard for a bed which has an arched board at the top.  In order to mark off the cut, I laid the board on the ground, staked one end of a cord to the ground, and swung the other end of the cord through a circular arc, holding a pencil at the appropriate distance.  If the board was 76” long and the circular arc comes down 3” from the top on each side as shown, what length rope did I use to mark off the cut (or, what is the radius of the circular arc)?

Solution #1:  Geometry - the products of the pieces of intersecting chords are equal (Craig)

Solution #2: Analytical Geometry - formula of circle (Tarplee, Sweet, Kefover

Solution #3: Trigonometry - Law of Sines (Tarplee)

Solution #4: Trigonometry - Law of Cosines (Tarplee)

Solution #5: Geometry - Pythagorean Theorem (Pomeroy)

Solution #7: Not Sure (Roberts) (used 8" instead of 3" drop)

r = (c^2/(4h) + h)/2

         c^2 + 4 h^2

       = -----------

             8h

= 76^2+4*8^2/8*8 = 94.25