MathDB

The length of the hypotenuse

BC

of a right triangle

ABC

a

, and on it the points

M

and

N

are taken such that

BM = NC = k

, with

k < a/2

. Assuming that (only) the data

a

and

k

are known, calculate: a) The value of the sum of the squares of the lengths

AM

and

AN

. b) The ratio of the areas of triangles

ABC

and

AMN

. c) The area enclosed by the circle that passes through the points

A, M' , N'

, where

M'

is the orthogonal projection of

M

onto

AC

and

N'

that of

N

onto

AB

Problem Statement