Geometry / Mr. Hansen
March 2004
[rev. 3/15/2020; 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



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, EJ, EH, EK


Note:  The angles are straightforward, but finding the radius (EB or EC) is a bit challenging. Hint: EBJC is a kite. After you find EB (which equals EC), you should find that EJ, EH, and EK are not hard to compute.

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.









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?




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