MathDB

Sharygin CR 2019 P18

Source: Sharygin CR 2019 P18 (Grade 10 - 11)

March 6, 2019

geometry

Problem Statement

A quadrilateral

ABCD

without parallel sidelines is circumscribed around a circle centered at

I

. Let

K, L, M

and

N

be the midpoints of

AB, BC, CD

and

DA

respectively. It is known that

AB \cdot CD = 4IK \cdot IM

. Prove that

BC \cdot AD = 4IL \cdot IN