I've been obsessed lately with Euclidea, an app that turns compass-and-straightedge constructions into puzzles. Here's a puzzle inspired by Euclidea
( Read more... )
There was some other online game I played a couple of years ago that was similar. Good times.
a.i.: Draw a circle centered on P. That will intersect l in two places, call those p1 and p2. Draw a circle centered on p1 that goes through p2, and a circle centered on p2 that goes through p1. Those two circles will intersect in two places above and below l. Draw a line connecting those two points, and that line will be perpendicular to l and go through P.
a.ii: Needed the first hint for this one. Draw a circle that passes through L at P, as well as at some other point, call it P'. Draw a line through the center of the circle and P', which will intersect the circle at point C. Draw a line through C and P.
b.i: Draw a circle around P that intersects l at two places, C1 and C2. Draw a circle at C1 that intersects C2, and vice versa. Draw a line between P and the intersection of C1 and C2.
Figured it out. Pick a point on l that's not right below P, call it L1, and draw a circle centered on L1 through P. This will intersect l on the other side of P at point L2. Draw a circle on L2 through P. The two circles will intersect at P, and also on the other side of l at P2. A line through P and P2 will be perpendicular to L.
Got it! Nicely done. PotD's 407 (tough) and 408 (not as tough) are recent Geometry puzzles that still want for a solution, if you're looking for a challenge.
Comments 4
a.i.: Draw a circle centered on P. That will intersect l in two places, call those p1 and p2. Draw a circle centered on p1 that goes through p2, and a circle centered on p2 that goes through p1. Those two circles will intersect in two places above and below l. Draw a line connecting those two points, and that line will be perpendicular to l and go through P.
a.ii: Needed the first hint for this one. Draw a circle that passes through L at P, as well as at some other point, call it P'. Draw a line through the center of the circle and P', which will intersect the circle at point C. Draw a line through C and P.
b.i: Draw a circle around P that intersects l at two places, C1 and C2. Draw a circle at C1 that intersects C2, and vice versa. Draw a line between P and the intersection of C1 and C2.
Reply
Reply
Reply
Reply
Leave a comment