MathDB

6

Part of 2020 Novosibirsk Oral Olympiad in Geometry

Problems(2)

<A'B'C'=? angle bisectors, <B=120^o (2020 Novosibirsk Oral Geo Oly 7.6)

Source:

4/27/2021
Angle bisectors AA′,BB′AA', BB'and CC′CC' are drawn in triangle ABCABC with angle ∠B=120o\angle B= 120^o. Find ∠A′B′C′\angle A'B'C'.
geometryangle bisectorangles
equal angles, tangents of circumcircle (2020 Novosibirsk Oral Geo Oly 9.6)

Source:

5/24/2021
In triangle ABCABC, point MM is the midpoint of BCBC, PP the point of intersection of the tangents at points BB and CC of the circumscribed circle of ABCABC, NN is the midpoint of the segment MPMP. The segment ANAN meets the circumcircle ABCABC at the point QQ. Prove that ∠PMQ=∠MAQ\angle PMQ = \angle MAQ.
geometryequal anglesTangents