MathDB

G2

Part of 2018 JBMO Shortlist

Problems(1)

< NA'T = < ADT wanted, starting with a right triangle, symmetric, projections

Source: JBMO Shortlist 2018 G2

7/22/2019
Let ABCABC be a right angled triangle with ∠A=90o\angle A = 90^o and ADAD its altitude. We draw parallel lines from DD to the vertical sides of the triangle and we call E,ZE, Z their points of intersection with ABAB and ACAC respectively. The parallel line from CC to EZEZ intersects the line ABAB at the point NN. Let A′A' be the symmetric of AA with respect to the line EZEZ and I,KI, K the projections of A′A' onto ABAB and ACAC respectively. If TT is the point of intersection of the lines IKIK and DEDE, prove that ∠NA′T=∠ADT\angle NA'T = \angle ADT.
geometryequal anglessymmetryright triangle