MathDB

Ratio of area is independent of the position of point

Source: Czech-Polish-Slovak 2012, P4

April 12, 2013

ratiogeometrycircumcirclearea of a trianglegeometry proposed

Problem Statement

Let

ABC

be a right angled triangle with hypotenuse

AB

and

P

be a point on the shorter arc

AC

of the circumcircle of triangle

ABC

. The line, perpendicuar to

CP

and passing through

C

, intersects

AP

BP

at points

K

and

L

respectively. Prove that the ratio of area of triangles

BKL

and

ACP

is independent of the position of point

P