Question

In triangle ABC, if D is any point on side BC, show that AB+BC+CA>2AD?
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Answer 1

QUESTION:—

• AM is a median of a triangle ABC. Is AB+BC+CA>2AM?

ANSWER:—

In triangle ABC, AM is a median.

In triangle ABM, AB+BM>AM… (1) [the sum of two sides of a triangle are greater than the third side].

In triangle ACM, AC+CM>AM… (2) [the sum of two sides of a triangle are greater than the third side].

Add (1) and (2) to get

AB+BM+AC+CM>AM+AM, or

AB+(BM+CM)+AC>2AM, or

AB+BC+CA>2AM. Proved