MathDB

1

Part of 2017 Bulgaria JBMO TST

Problems(2)

Geometry with fixed angles

Source: Bulgaria JBMO TST 2017 P1 Day 1

8/26/2019
Given is a triangle ABCABC and let AA1AA_1, BB1BB_1 be angle bisectors. It turned out that ∠AA1B=24∘\angle AA_1B=24^{\circ} and ∠BB1A=18∘\angle BB_1A=18^{\circ}. Find the ratio ∠BAC:∠ACB:∠ABC\angle BAC:\angle ACB:\angle ABC.
geometrygeometry proposed
Classical NT equation

Source: Bulgaria JBMO TST 2017 P1 Day 2

8/26/2019
Find all positive integers a,b,c,d a, b, c, d so that a2+b2+c2+d2=13⋅4n a^2+b^2+c^2+d^2=13 \cdot 4^n
number theory proposednumber theory