MathDB

4

Part of 2020 Novosibirsk Oral Olympiad in Geometry

Problems(2)

perp. bisector of NM bisects AB, altitudes (2020 Novosibirsk Oral Geo Oly 7.4)

Source:

4/27/2021
The altitudes ANAN and BMBM are drawn in triangle ABCABC. Prove that the perpendicular bisector to the segment NMNM divides the segment ABAB in half.
geometrybisects segment
equal angles in square, midpoints (2020 Novosibirsk Oral Geo Oly 9.4)

Source:

5/24/2021
Points EE and FF are the midpoints of sides BCBC and CDCD of square ABCDABCD, respectively. Lines AEAE and BFBF meet at point PP. Prove that ∠PDA=∠AED\angle PDA = \angle AED.
equal anglessquare