MathDB

Let

ABC

be a triangle with

BC > AC > AB

. Let

A',B',C'

be feet of perpendiculars from

A,B,C

BC,AC,AB

, such that AA' \equal{} BB' \equal{} CC' \equal{} x. Prove that: a) If

ABC\sim A'B'C'

then x \equal{} 2r b) Prove that if

A',B'

and

C'

are collinear, then x \equal{} R \plus{} d or x \equal{} R \minus{} d. (In this problem

R

is the radius of circumcircle,

r

is radius of incircle and d \equal{} OI)

Problem Statement