In triangle ABC the line :CD is altitude on :AB,if the point : P is on the side :CD. the line AP intersect :CB in the point :Q and the line: BP intersect CA in the point :R
how to prove that angle RDC= angle QDC?
The book "Challenging Problems in Geometry" by Posamentier and Salkind, part of which is available in Google books, has this question as problem 8-25 on p. 41. It suggests proving this fact using Ceva's theorem. A solution using this theorem, as well as a couple of other solutions, is available here on Yahoo answers.