MathDB

2008.7

Part of Ukraine Correspondence MO - geometry

Problems(1)

angles wanted, <ABD = <CBD, 3<ACE = 2<BCE, CD = DE = CH

Source: 2008 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p7

4/28/2021
On the sides ACAC and ABAB of the triangle ABCABC, the points DD and EE were chosen such that ∠ABD=∠CBD\angle ABD =\angle CBD and 3∠ACE=2∠BCE3 \angle ACE = 2\angle BCE. Let HH be the point of intersection of BDBD and CECE, and CD=DE=CHCD = DE = CH. Find the angles of triangle ABCABC.
geometryequal anglesequal segmentsUkraine Correspondence