2

Part of 2021 Auckland Mathematical Olympiad

Problems(2)

2 out of 5 inside an equilateral of side 2 (2021 Auckland MO J2)

Source:

Given five points inside an equilateral triangle of side length

2

, show that there are two points whose distance from each other is at most

1

Equilateralgeometrydistance

angles wanted in right triangle, reflection (2021 Auckland MO S2)

Source:

ABC

is the right angled triangle with the vertex

C

at the right angle. Let

P

be the point of reflection of

C

AB

. It is known that

P

and two midpoints of two sides of

ABC

lie on a line. Find the angles of the triangle.

geometrygeometric transformationreflection