An IMO Problem Involving Concurrency

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

Let A, B, C, and D be distinct points on a line. Let the circles with diameters AC and BD intersect at points X and Y. Let the intersection of BC and XY be Z. Let P be a point on XY different from Z. Let CP intersect the circle with diameter AC at the point M different from C and let BP intersect the circle with diameter BD at the point N different from B. Then AM, DN, and XY are concurrent.

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA


Snapshots


Details

This is problem 1 from the 36-th International Mathematical Olympiad.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send