In the given figure ABC is a triangle. X is a point on the side BC. Prove that 2AX

September 2023 1 7 Report

In the given figure ABC is a triangle. X is a point on the side BC. Prove that 2AX < AB + BC + CA.

Answer:

Given: △ABC in which D is a point on BC

To prove: AB+BC+CA>2AD

Construction: AD is joined.

Proof: In △ABD,AB+BD>AD [∵, the sum of any

two sides of a triangle isalways greater than the third side] ---(1)

In △ADC,AC+DC>AD [∵, the sum of any two sides of a triangle is always greater than the third side] ---- (2)

Adding (1) and (2) we get,

AB+BD+AC+DC>AD+AD

⇒AB+(BD+DC)+AC>2AD

⇒AB+BC+AC>2AD

Hence proved

Step-by-step explanation:

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