Geometry / Mr. Hansen March 2004 [fonts corrected 2/16/2009, small error in Chris’s puzzle corrected 2/17/2009] Name: _______________________

Angle-Arc Puzzles Created by Students and Mr. Hansen

 1. Chris M.’s award-winning puzzle for 2004, edited by Mr. Hansen Given: Circle E, = 65°, arc GF = 30°, arc GB = 110°, JC = 6, HP = 3, NK = 4 Find: , , , , , , , EB, EH, EK   Note:  The angles are straightforward, but I cannot find a way to find the radius (EB or EC) without using the Law of Cosines, a topic from Algebra II. If I tell you that the radius is approximately 5.0346, any geometry student should be able to find not only EH and EK, as required by Chris’s original puzzle, but EJ as well. The original puzzle had JC = 7, but the diagram turns out to be impossible in that case. Using JC = 6 as above makes everything work out. If you would like a real challenge (probably suitable only for Algebra II students and above), try to compute AN, AP, and AE.

 2. An easier puzzle by Nico C. (edited by Mr. Hansen) Given: Circle P with points of tangency at Q and O, arc ML = 50°, arc LO = 75° Find: All arcs and angles Note:    The original version of this puzzle had arc LO = 100°. Can you prove that that would be impossible? 3. A puzzle by Mr. Hansen that is not hard if you look at it in the right way Given: Circles C and D, points of tangency at A and T, = 15°, EG = FG Find: 