If $O$ is a point in the exterior of $△ A B C$ , show that $2 (O A + O B + O C) > (A B + B C + C A)$ .

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Solution

Given
$2 (O A + O B + O C) > (A B + B C + C O)$
given question is wrong it should be
$2 (O A + O B + O C) > (A B + B C + C A)$

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Similar questions

Q. If O is a point in the exterior of ∆ABC, show that 2(OA + OB + OC) > (AB + BC + CA).

Figure

Q. In figure,

O

is an interior point of

Δ A B C

. Show that:

A B + B C + C A < 2 (O A + O B + O C)

If $O$ is a point within triangle $A B C$ , show that,

$If O is a point within Δ A B C, show that (i) AB + AC > O B + O C (ii) AB + BC + CA > O A + O B + O C (iii) OA + OB + OC > \frac{1}{2} (A B + B C + C A .)$

Q. If

O

is a point within

Δ

ABC then show that :
1)

A B + A C = O B + O C

A B + B C + C A > O A + O B + O C

O A + O B + O C > \frac{1}{2} (A B + B C + C A)

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If O is a point in the exterior of △ABC, show that 2(OA+OB+OC)>(AB+BC+CA).

Given 2(OA+OB+OC)>(AB+BC+CO)given question is wrong it should be2(OA+OB+OC)>(AB+BC+CA)

If $O$ is a point in the exterior of $△ A B C$ , show that $2 (O A + O B + O C) > (A B + B C + C A)$ .

Given
$2 (O A + O B + O C) > (A B + B C + C O)$
given question is wrong it should be
$2 (O A + O B + O C) > (A B + B C + C A)$