The internal bisector of of meets side at

MATHEMATICS · Multi correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

The internal bisector of

\angle A

of

\triangle ABC

meets side

BC

at

D

. A line drawn through

D

perpendicular to

AD

intersects side

AC

at

E

and side

AB

at

F

. If

a

,

b

, and

c

represent the sides of

\triangle ABC

, then (1)

AE

is the H.M. of

b

and

c

. (2)

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

(3)

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

(4)

\triangle AEF

is isosceles.

Related theory

Browse the problem library