MathDB

Given a triangle

ABC

with angle

A

obtuse and with altitudes of length

h

and

k

as shown in the diagram, prove that

a+h\ge b+k

. Find under what conditions

a+h=b+k

. [asy] size(6cm);
pair A = dir(105), C = dir(170), B = dir(10), D = foot(B, A, C), E = foot(A, B, C);
draw(A--B--C--cycle); draw(B--D--A--E);
dot(A); dot(B); dot(C); dot(D); dot(E);
label("

A

", A, dir(110)); label("

B

", B, B); label("

C

", C, C); label("

D

", D, D); label("

E

", E, dir(45));
label("

h

", A--E, dir(0)); label("

k

", B--D, dir(45)); [/asy]

Problem Statement