MathDB

1

Part of 2021 Oral Moscow Geometry Olympiad

Problems(2)

tan<ABD wanted on a grid paper

Source: 2021 Oral Moscow Geometry Olympiad grades 8-9 p1

5/24/2021
Points A,B,C,DA,B,C,D have been marked on checkered paper (see fig.). Find the tangent of the angle ABDABD. https://cdn.artofproblemsolving.com/attachments/6/1/eeb98ccdee801361f9f66b8f6b2da4714e659f.png
geometrytrigonometrygrid
ad= bc, distances from a point of circumcircle to lines of inscribed ABCD

Source: 2021 Oral Moscow Geometry Olympiad grades 10-11 p1

5/24/2021
Quadrilateral ABCDABCD is inscribed in a circle, EE is an arbitrary point of this circle. It is known that distances from point EE to lines AB,AC,BDAB, AC, BD and CDCD are equal to a,b,ca, b, c and dd respectively. Prove that ad=bcad= bc.
geometrycircumcirclecyclic quadrilateral