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RS = \sqrt2 SQ if AD=CR , CR _|_ AB, ABC right isosceles

Source: Indonesia INAMO Shortlist 2008 G2

August 25, 2021

isoscelesequal segmentsgeometry

Problem Statement

Let

ABC

be an isosceles triangle right at

C

and

P

any point on

CB

. Let also

Q

be the midpoint of

AB

and

R, S

be the points on

AP

such that

CR

is perpendicular to

AP

and

|AS|=|CR|

. Prove that the

|RS| = \sqrt2 |SQ|