Question

in an isosceles right angled triangle a straight line is drawn from the middle point of one of the equal sides to the opposite vertex. show that it divides the angle into two parts whose cotangents are 2 and 3

Answer 1

Answer:

Let ABC be the triangle, right angled at C, and D be the mid-point of AC. Join DB.

Since AC =BC =x, we have

DC=

2

1

​

AC=

2

1

​

BC=

2

x

​

Also ∠CAB=∠CBA=45

0

If ∠DBC=θ and ∠DBA=ϕ,

tanϕ=

BC

DC

​

=

x

x/2

​

=

2

1

​

tanϕ=tan(45

0

−θ)=

1+tanθ

1−tanθ

​

or tanϕ=

1+1/2

1−1/2

​

=

3

1

​

∴cotθ=2,cotϕ=3