Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let ABC be a triangle with AB = AC. If D is the mid-point of BC, E foot of perpendicular drawn from D to AC and F is mid point of DE. Find the angle between AF and BE.<s

Let ABC be a triangle with AB = AC. If D is the mid-point of BC, E foot of perpendicular drawn from D to AC and F is mid point of DE. Find the angle between AF and BE.

Option: 1

60^{\circ}


Option: 2

75^{\circ}


Option: 3

90^{\circ}


Option: 4

105^{\circ}


Answers (1)

best_answer

Coordinates of point E are \mathrm{\left(\frac{a b^2}{a^2+b^2}, \frac{a^2 b}{a^2+b^2}\right)}

\therefore Coordinates of point F are  \mathrm{\left(\frac{a b^2}{2\left(a^2+b^2\right)}, \frac{a^2 b}{2\left(a^2+b^2\right)}\right)}                         

Slope of AF =

                     \mathrm{\frac{\frac{a^2 b}{2\left(a^2+b^2\right)}-b}{\frac{a b^2}{2\left(a^2+b^2\right)}}=-\frac{a^2 b+2 b^3}{a b^2}=-\frac{a^2+2 b^2}{a b}}

Slope of BE = 

                      \mathrm{\frac{\frac{a^2 b}{a^2+b^2}}{\frac{a b^2}{a^2+b^2}+a}=\frac{a b}{a^2+2 b^2}}

As the product of slopes of AF and BE = –1

\therefore AF and BE are perpendicular.

Posted by

Gunjita

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question