MathDB

1

Part of 2019 Oral Moscow Geometry Olympiad

Problems(2)

distance of a point from incircle equals to a diameter of incircle

Source: 2019 Oral Moscow Geometry Olympiad grades 8-9 p1

5/21/2019
In the triangle ABC,IABC, I is the center of the inscribed circle, point MM lies on the side of BCBC, with ∠BIM=90o\angle BIM = 90^o. Prove that the distance from point MM to line ABAB is equal to the diameter of the circle inscribed in triangle ABCABC
geometrydiameterincircleincenterdistance
angle chasing related to circle inscribed in square

Source: 2019 Oral Moscow Geometry Olympiad grades 10-11 p1

5/22/2019
Circle inscribed in square ABCDABCD , is tangent to sides ABAB and CDCD at points MM and KK respectively. Line BKBK intersects this circle at the point L,XL, X is the midpoint of KLKL. Find the angle ∠MXK\angle MXK .
geometrysquareincircleangle