MathDB
concurrent wanted, <CBP =ACB, <QCB = <CBA., 2 circles

Source: 2020 IberoAmerican p1

November 17, 2020
geometryconcurrencyconcurrent

Problem Statement

Let ABCABC be an acute scalene triangle such that AB<ACAB <AC. The midpoints of sides ABAB and ACAC are MM and NN, respectively. Let PP and QQ be points on the line MNMN such that ∠CBP=∠ACB\angle CBP = \angle ACB and ∠QCB=∠CBA\angle QCB = \angle CBA. The circumscribed circle of triangle ABPABP intersects line ACAC at DD (D≠AD\ne A) and the circumscribed circle of triangle AQCAQC intersects line ABAB at EE (E≠AE \ne A). Show that lines BC,DP,BC, DP, and EQEQ are concurrent.
Nicolás De la Hoz, Colombia
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