MathDB

4

Part of 2021 SAFEST Olympiad

Problems(1)

<KCD = <DAC if DB = DC

Source: 3rd SAFEST Olympiad (July 2021) p4, South African - Estonian IMO teams

9/9/2021
Let ABCABC be a triangle with AB>ACAB > AC. Let DD be a point on the side ABAB such that DB=DCDB = DC and let MM be the midpoint of ACAC. The line parallel to BCBC passing through DD intersects the line BMBM in KK. Show that ∠KCD=∠DAC.\angle KCD = \angle DAC.
geometryequal anglesequal segments