P, Q and R are the mid-points of sides BC, CA and AB respectively of ∆ABC - Maths - Triangles

Question

P, Q and R are the mid-points of sides BC, CA and AB respectively
of ∆ABC Prove that : AC + 2BQ > AB + BC

Muskaan Talwar · Accepted Answer

Dear Student,
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_59d50b4b2cd1f%20png">

In △ABQ,AQ+BQ>AB Sum of any two sides of triangle is greater than third sideIn △CBQ,CQ+BQ>BC Sum of any two sides of triangle is greater than third sideThus, AQ+BQ+CQ+BQ>AB+BCi
e  AQ+CQ+2BQ>AB+BCi e  AC+2 BQ>AB+BC

Regards

P, Q and R are the mid-points of sides BC, CA and AB respectively of ∆ABC. Prove that : AC + 2BQ > AB + BC