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d(I_1, AD)+ d(I_2, AD)=1/4 BC, bisectors in right ABC (1996 Romania NMO VII p4)

Source:

August 13, 2024

geometryright triangle

Problem Statement

In the right triangle

ABC

(

m ( \angle A) = 90^o

)

D

is the foot of the altitude from

A

. The bisectors of the angles

ABD

and

ADB

intersect in

I_1

and the bisectors of the angles

ACD

and

ADC

I_2

. Find the angles of the triangle if the sum of distances from

I_1

and

I_2

AD

is equal to

\frac14

of the length of

BC