MathDB

5

Part of 2020 Novosibirsk Oral Olympiad in Geometry

Problems(2)

CK_|_AB if AK=KB+PC, BC=AP, <APC +<ABC=180^o (2020 Novosibirsk Oral Geo Oly 7.5)

Source:

4/27/2021
Point PP is chosen inside triangle ABCABC so that ∠APC+∠ABC=180o\angle APC+\angle ABC=180^o and BC=AP.BC=AP. On the side ABAB, a point KK is chosen such that AK=KB+PCAK = KB + PC. Prove that CK⊥ABCK \perp AB.
geometryperpendicularequal segments
midpoint wanted, perp. bisectors (2020 Novosibirsk Oral Geo Oly 8.5)

Source:

5/20/2021
Line ℓ\ell is perpendicular to one of the medians of the triangle. The median perpendiculars to the sides of this triangle intersect the line ℓ\ell at three points. Prove that one of them is the midpoint of the segment formed by the other two.
geometryperpendicular bisectormidpoint