CEMC Fermat, 1998

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

Square $ABCD$ has sides of length $14$ . A circle is drawn through $A$ and $D$ so that it is tangent to $BC$ , as shown. What is the radius of the circle?

(A) $8.5$ (B) $8.75$ (C) $9$ (D) $9.25$ (E) $9.5$

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.