MathDB

A computational geometry, midpoint of a side

Source: Iran TST 2007, Day 1

May 7, 2007

geometrytrigonometrycircumcircleangle bisectorgeometry proposed

Problem Statement

In triangle

ABC

M

is midpoint of

AC

, and

D

is a point on

BC

such that

DB=DM

. We know that

2BC^{2}-AC^{2}=AB.AC

. Prove that

BD.DC=\frac{AC^{2}.AB}{2(AB+AC)}