In ∆ABC, ∠B=35°,∠C=65° and the bisector of ∠BAC meets BC in X. Arrange AX, BX and CX in descending order.

Given: In ∆ABC, B=35°,C=65° and BAX = XAC

To find: Relation between AX, BX and CX in descending order.

In ∆ABC, by the angle sum property, we have

A + B + C = 180°

A + 35° + 65° = 180°

A + 100° = 180°

A = 80°

But BAX = A

= × 80° = 40°

Now in ∆ABX,

B = 35°

BAX = 40

And BXA = 180° - 35° - 40°

= 105°

So, in ∆ABX,

B is smallest, so the side opposite is smallest, ie AX is smallest side.

AX < BX …(1)

Now consider ∆AXC,

CAX = × A

=× 80° = 40°

AXC = 180° - 40° - 65°

= 180° - 105° = 75°

Hence, in ∆AXC we have,

CAX = 40°, C = 65°, AXC =75°

∴∠CAX is smallest in AXC

So the side opposite to CAX is shortest

Ie CX is shortest

CX <AX …. (2)

From 1 and 2 ,

BX > AX > CX

This is required descending order

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
NCERT | Triangle Inequalities47 mins
Know More About Triangle Inequalities28 mins
NCERT | Tricks to Apply Triangle Inequalities45 mins
Champ Quiz | Area of Triangle53 mins
NCERT | Imp. Qs. on Area of Parallelogram and Triangles43 mins
Champ Quiz | Mastering Triangles44 mins
RD Sharma | Important Proofs in Triangles28 mins
Quiz | Area of Parallelogram and Triangles43 mins
Quiz | Area and Parallelogram46 mins
NCERT | Imp Qs on Area of Parallelogram And Triangles44 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses