CEMC Hypatia, 2008

Geometry Difficulty 2.0 Junior Prove it Canada

There is a point $K$ on $AB$ such that the area of $\triangle KBC$ equals the area of quadrilateral $KADC$ . Determine the length of $BK$ .

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.