Let K (on an extension of AB) be the center of the circumcircle of triangle OEA, and let the circumradius be r. Let alpha angle CAO angle KAO be the external half-angle at A. Note that these two parameters are dependent: triangle KAE is isosceles with legs r, base 2, and base angles 2alpha; thus, rcos 2alpha 1. Since triangle AKO is isosceles with angle KOA angle KAO alpha angle CAO, we have OK parallel CA. This guarantees triangle OKB sim triangle EAB, and we see fracOK2 fracbkab implies fracr2 fracABrAB implies AB frac2 rr-2 (Observe that this requires r 2.) By the Angle Bisector Theorem in triangle ABC, fracaeab fraccecb implies frac2ABfrac3CB implies CB frac3rr-2, via the Law of Cosines at (internal) angle A in triangle ABC, cosleft(pi-2alpharight) fracAC2AB2-BC22acab fracr2-5r5r(r-2 recalling that rcos 2alpha1 (and, of course, that cos(pi-2alpha)-cos 2alpha we have -frac1r fracr2-5r5r(r-2) implies (r-1 r-3) - Cost-Effective Prices for Essay Services: Try our service and be able to enjoy huge savings our prices are highly affordable and our discount deals are simply outstanding. Irrespective of how tricky the instructions are or how difficult the subject is, our essay writing experts will always find a way to deliver the finest work. Any Type of Writing Assignment, Any Subject. Whatever writing assignment you need to do, you can order it here. We complete academic assignments of any kind, even non-typical orders like PowerPoint presentations and Math problems.
As for the 300-word limit, Freeman says, most of my faculty and admissions professionals are not sure that any 17-year-old has much more than 300 well thought-out words to say on any topic.
Be aware that you should not reiterate any portion of the essay you used for the Common Application. Using one of the themes below as a starting point, write about a person, event, or experience that helped you define one of your values or in some way changed how you approach the world.