Tag Archives: plane geometry

Unlawful Distance

This is a puzzle from the A+Click site.

“There is a fault with the cruise control on Hank’s car such that the speed continuously and linearly increases with time.  When he starts off the speed is set to exactly 60 mph.  He is driving on a long straight route with the radio on at full blast and he is not paying any attention to his speed.  After 3 hours he notices that his speed has now reached 80 mph.  For how many miles did he drive above the state speed limit of 70 mph?

Answer Choices:            125 miles     112.5 miles     105 miles     99.5 miles”

Answer.

See Unlawful Distance for solutions.

Wittenbauer’s Parallelogram

This is a lovely result from Futility Closet.

“Draw an arbitrary quadrilateral and divide each of its sides into three equal parts. Draw a line through adjacent points of trisection on either side of each vertex and you’ll have a parallelogram.

Discovered by Austrian engineer Ferdinand Wittenbauer.”

Find a proof.

See Wittenbauer’s Parallelogram for a solution.

Two Squares in a Circle

This puzzle, from another set of seven challenges assembled by Presh Talwalkar, turned out to be very challenging for me.

“This is a fun problem I saw on Reddit AskMath. A circle contains two squares with sides of 4 and 2 cm that overlap at one point, as shown. What is the area of the circle?”

This took me quite a while to figure out, but I relied on another problem I had posted earlier.

Answer.

See Two Squares in a Circle for solutions.

Chinese Quadrilateral Puzzle

This is another intimidating puzzle from Presh Talwalkar:

“Thanks to Eric from Miami for suggesting this problem and sending a solution!

From a 5th grade Chinese textbook: In the quadrilateral ABCD, angle A = 90°, angle ABD = 40°, angle BDC = 5°, angle C = 45°, and the length of AB is 6. Find the area of the quadrilateral ABCD.”

Answer.

See the Chinese Quadrilateral Puzzle for solutions.

Ubiquitous 60 Degree Problem

This is an interesting problem from the Canadian Mathematical Society’s 2001 Olymon.

“Suppose that XTY is a straight line and that TU and TV are two rays emanating from T for which XTU = UTV = VTY = 60º. Suppose that P, Q and R are respective points on the rays TY, TU and TV for which PQ = PR. Prove that QPR = 60º.”

See the Ubiquitous 60 Degree Problem