MathDB

2013 preRMO p19, computational with right triangle and ratio of areas

Source:

August 8, 2019

ratioareasright triangle

Problem Statement

In a triangle

ABC

with

\angle BC A = 90^o

, the perpendicular bisector of

AB

intersects segments

AB

and

AC

X

and

Y

, respectively. If the ratio of the area of quadrilateral

BXYC

to the area of triangle

ABC

13 : 18

and

BC = 12

then what is the length of

AC