Problem

Problem

Internal bisector of

\angle A

of

\Delta ABC

meets side

BC

at

D

. A line drawn through

D

perpendicular to

AD

intersects the side

AC

at

E

and side

AB

at

F

. If

a, b, c

represent sides of

\Delta ABC

, then [More than one correct option 2006] a.

AE

is HM of

b

and

c

b.

AD = \frac{2bc}{b+c} \cos \frac{A}{2}

c.

EF = \frac{4bc}{b+c} \sin \frac{A}{2}

d.

\Delta AEF

is isosceles

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